Can we design social herding to enhance cooperation?
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Schweitzer, Frank
Payoff‐dependent adoption of strategies is one of the most common assumptions in evolutionary game theory. If individuals are able to observe both the strategies and the payoffs of their neighbors, they tend to switch to the most successful strategy. This, however, often results in a dilemma situation if payoffs depend on the strategies chosen by the counterparts. If everyone tries to maximize the personal payoff, individuals may end up with obtaining less than expected. Evolutionary game theory has suggested different routes out of this dilemma situation. We propose a rarely explored solution, namely to provide individuals with less information, instead of more information. In the absence of full information about neighbors' strategies and resulting payoffs, individuals tend to simply follow the action of the majority, without calculating all consequences. This kind of social herding leads to a strong amplification of locally dominating strategies. At the same time, the tension between the most successful and the most frequently used strategy may increase. Using an agent‐based model that combines elements of strategic decisions and social herding, we explore the conditions under which less information may help to avoid social dilemma. We also design ICT‐based interaction mechanisms for individuals, to enhance cooperation.
 And with this I would like to welcome Frank Schweitzer, who is of ETH Zurich. Now he is the Office of Physicists as well, but now he is very serious about economics. And he is a big team trying to focus on network aspects and dynamic aspects, non-equilibrium models in economics. And also on large-scale data mining has come up with a number of very interesting and innovative publications in the past years. And actually there is another workshop that I'd like to mention, which is Economics on the Move. And I'm pretty sure that would be interesting for you as well, so feel happy to try. Thank you very much, Frank. Are you ready to go? Yeah, okay. Good afternoon, everyone. It's my great pleasure to present some work from the Chair of Systems Design. Actually our research is mostly concerned with what we call data-driven modeling. We are interested in big data, as Dirk just said. But I opted out to talk about this for reasons. The first one I don't dare to compare and compete myself with these people here, like Alex Vespignani. The second thing, I personally get bored to always talk about cyber emotions and these kind of things. The third reason I thought for a workshop on agent-based modeling, it would be appropriate to present an agent-based model that can be also served analytically. And fourth, I thought for a workshop, it would be appropriate to present some work in progress. And that's what we do now. The question is, can we design social hurting to enhance cooperation? The take-home message is yes. And there are at least three different approaches that we are following in these three different papers. Two of these I will shortly discuss today. And the third one is probably mentioned tomorrow by Hans Söntzers. But of course, I wouldn't have suggested this topic if we were not able to enhance cooperation by means of social hurting. The question is, then, what's the problem in detail, although what's the model that we have chosen to describe the problem, what is the optimal design to enhance cooperation and the fewer extensions? So let me go first into the problem. Social hurting and cooperation are not that different. As you can, for example, see in this little picture here, there are lots of communalities. I mean, some of you might be able to see what this actually is. Now we see it a bit better, right? So, okay. So both social hurting and cooperation have in common that individual decisions are made based on the observed or the assumed actions of others. There is the example of buying a product because you observe someone else is buying the product. You don't know about the reasons, of course, but you might also guess about the reasons. There are other examples here. But more important are the differences. Social hurting basically describes a very simple imitation process, all of what we call contagious behavior. That means an agent I copies the action of another agent J without knowing the consequences. That's a very important thing. So the assumption for social hurting is there is no information available on the side of I, but maybe J has all the information about choosing this product and therefore I simply copies the decision of J. And this, of course, implies that I and J are somehow similar. They have some profile features in common or they have similar responses. And then it also makes sense to copy decisions or actions of others because this reduces your own risk of making the wrong decision. Cooperation, on the other hand, is a very different behavior because it's based on a strategic decision to maximize the payoff. That means I, agent I, chooses the action that I wants to do based on what J is doing in response to J. And the action is chosen in such a way that the payoff is maximized. The assumption here is differently. The assumption is that there is full information on the side of I. I knows all the alternatives. I is able to calculate every payoff correctly and then I can compare both payoffs or all the payoffs. And this, of course, is based on the assumption as well that the payoffs can be calculated. And you can think of very many situations. Think of the picture I have just shown where you have difficulties to calculate the payoff for yourself, right? But the intuition, if you compare social hurting and strategic behavior, is it's always better to have more information. If you are able to choose among all the alternatives and you know all the outcome, you reduce your own risk of making the wrong decision, choosing the wrong action. And therefore, it's much better if you have the full information available. That's at least what we think intuitively. But more is not always better and that's also true for the available information. I want to present two counter examples to just give you a flavor of where information and in particular more information, hemp-ass finding the better solution. In the first example, we referred to the phenomenon of the wisdom of crowds. We did experiments with humans together with Sturck and published in this paper here. We also developed an agent-based model. The situation was the following. Individuals had to make a guess on an arbitrary question, how long is it, what's the length of the border of Switzerland, for example. And then they had to do this in five rounds and they were treated with three different information regimes. In the first case, they had no information available about the guesses of other people. In the second case, they had the aggregated information available about the guesses of others, so what's the mean value of all the guesses. And in the third case, they had all the trajectories available of how the others have guessed the length of the border of Switzerland and how they have adjusted their values. And then individuals got to respond to this. It's perfectly fine if you cannot read the numbers in this picture. The most important thing is here in this little bar on the bottom. If we use a measure for the quality of the guess, the wisdom of crowd indicators, and we see that the wisdom of crowd indicator severely declines the more information we give to the humans. That means the prediction usually becomes less accurate if people have more information available about the guesses of others. And the case that makes it even worse is if you ask people about this, then they are convinced that the wrong results they converge to actually is a better one because they saw each other converging to something. That means this is a real tricky threat in this kind of phenomenon. Everyone converges to the wrong result and at the same time, we are all convinced that we have converged to the right result. There are two important mistakes involved in this presentation of more information. The second example comes also from a theoretical model where we try to describe network formation in an agent-based model. These agents are described by utility and they had to create links. There are two different scenarios here. One is called incremental improvement. The other one, best response. In an incremental improvement, agent i tests if the utility will increase and agent j tests if the utility will increase. And if both of these utilities increase, they decide to form a link. In the best response case, agent i says, well, of course, the utility increased, but maybe it will increase more if I link to another agent. So every agent systematically checks all other agents in the system to find out what is the most optimal agent to create a link to. It means in best response case, you have all the information available. What you see here is the more information you have available, the worse the performance of the system is. We know and can also verify this by mathematical proof that the optimal network looks like this, more or less a fully connected network among the agent. That's incremental improvement. That's best response. You see that the structures we reach are very different from the real, from the known optimal state. That means the system gets trapped in a suboptimal state, and because agents are always pointed back because of all this information to this suboptimal state, the system is never able to leave. These are two examples where we see more information may not enhance the situation. Then, of course, our hypothesis is maybe less information is a better one. We use this as a hypothesis because we assume that less information may avoid the stateloc situation that I have just described, or this log in in a suboptimal state. In particular, we want to explore one important idea here, namely that we want to overcome a social dilemma by including social hurting to a behavior that is usually assumed as strategic behavior. This is a little graph I usually use to explain the situation. I learned that no one really understands this, so it doesn't matter if we are very short about this. Look at this dimension and let's assume that this axis measures the effort. This is the strategic dimension, for example, of calculating the payoff. We are here in the beginning of the state, so we might find a better state where negative means better, less effort, or even again. We have to overcome a series of suboptimal states along this way. If we instead include these other dimensions, then we might be able to find a detour that is, of course, longer, but maybe avoids climbing up this mountain of suboptimal states. At the end, because we go along this line, we end up in the same valley of positive of optimal states, but not going this way, but that way. We are trying to explore different mechanisms of getting into this direction. Most notably, I'd like to point out that we do a lot of work on emotional influence. Emotional influence is a specific representation of the social dimension here. I'm not going to talk about this, as I said in the beginning. Now, having said this as a motivation, what is the model we have used to describe this? Sorry for the many equations here. What we would like to do is we want to combine the social dimension, which is the social hurting, and the strategic dimension. We use a model of heterogeneous agent where each agent is described by two individual variables. This theta describes a strategy, whether the agent defects or whether it co-operates. Theta equals one means the agent co-operates. The second variable, theta, describes to what extent is the agent prone to social influence. So letter one is a continuous variable between zero and one. With respect to the strategic interaction, we assume that there is a number of simultaneous two-person games, and the payoff is described by this payoff matrix. There are these two strategies of agent i, and there are the two possible strategies of agent j, and then dependent of what i and j choose, you see these payoffs here. For the numbers, we use the so-called prisoner-stile lemma game, where the payoffs are ranked according to these inequalities. The important thing to notice is that t is the highest, like five, but two r is more than t plus s. That means if two agents decide to co-operate, this accumulative payoff is larger than if one agent decides to co-operate, and the other one decides to defect. But if you see it from the perspective of the individual agent, defection is always the best strategy, because you get then five points if you meet a co-operator, and you get at least one if you meet a defector. So then based on this, we can now assume that n simultaneous games are played, and the payoff of the agent depends, of course, on its own strategy and on the number of co-operators and the number of defectors that he has met in these n independent games. So this is simply the straightforward expression of the payoff, dependent on whether I'm co-operating, then I get this, or whether I'm defecting, then I get this. So if we scale it here by n, then we get this, and the little f here is the local frequency of co-operators. That is going to be the important key variable here. Every agent is described with the neighborhood and interacts with other agents in its neighborhood, and the frequency of co-operators is the most important variable here. The payoff values are fixed. Now I have to include the social part into this, and this is done when agents are able to update their strategies. We have to talk about this transition rate. You read it as all the other equations, always from right to left. So the agent is in a state 1 minus theta, and it has to decide whether it switches to the opposite state, which is theta. And this depends on the number of co-operators in the neighborhood, and it also depends on how much the agent is prone to social influence. In order to combine this, we just have these two expressions here. You see, g represents a strategic component which is based on the payoff, whereas the f represents a social component which just results from the social hurting effect. And the theta combines the two. The theta is 1, then we are talking about hurting effects only. If the theta is 0, then we are talking about strategic considerations only. The question now is, what do we assume for the g and the a? I have given you here the equations. I am not going to present all the details. There are a few things you have to notice. The first one, it looks like a logic function. There is something in the exponent that is normalized. What is in the exponent? The payoff. The normalized payoff that the agent gets. What the agent is doing in the strategic case, it compares the payoff that the agent gets by choosing strategy theta with the payoff that the agent would get by choosing strategy 1 minus theta, which is the opposite. And then the agent probably follows that strategy that gives him the higher payoff. If you develop these expressions here, then you see that this is usually proportional to the difference in this payoff. For the social hurting part, we also have chosen a logic, logic function. And if you develop this here, then you get that it is proportional to the frequency of the guys doing the opposite of what am I doing. I am playing strategy 1 minus theta, then the other guys are playing strategy theta. And if I see very many agents in my neighborhood that are playing the opposite strategy, then because of the social hurting, I am more inclined to adopt their strategy. I do this only because I see that there are so many of these, and not because I know they have all the high payoffs. You understand? It can be all that they have the low payoff, but I do not know this. And here is a nonlinear function in front of this frequency, which we are going to use later on. So last slide with the nasty details. It's simply to show you what are the parameters we want to tune at the very end. We have chosen n equal to 4, because we also want to compare a mean field limit with a simulation on the lattice. That's why we took Q. And we have abbreviated these transition rates that I have explained on the previous side simply by these C and D values. C naught means I am a co-operator and I switch to defection, but in my neighborhood there are no co-operators. And C3 means I am a co-operator and I am switching to defection, but in my neighborhood there are 75% of co-operators. And now of course I have to describe these C's, and for the D's it's the similar thing. So as I have explained, each of these C's and D's transition rates is composed of two of these terms here. One term related to the strategic behavior and the other one related to the social hurting. For the strategic behavior we just go back to slides where I have printed the payoff of the agent. This is a straightforward expression of what is the payoff if I have three co-operators in my neighborhood out of four and so on and so on. The same is true for the D. And for the hurting part, C and D, I have simply used these alpha values. That means I did not specify them. Of course I can assume later that it is directly proportional to the frequency here, but I want to make use of all the non-linear functions, therefore I specify it in this very abstract way. So what are the only parameters on this slide that are not known? Alpha 0, alpha 1 and alpha 2. Well, everything else is determined by what we have in the game. Last slide to wrap up with this. If you specify it like this, then we are able to derive a mean-field equation for the global frequency of co-operators. This has a form of a fitness selection equation. E1 is the fitness associated with the co-operators and E0 is the fitness associated with the defectors. You see that of course the share of the co-operators increases if the fitness of the co-operators is larger than the fitness of the defectors. That is one thing that you get immediately out of the mean-field equation and the E1 and the E0 are known to us because they are simply specific functions of these C and D values that I have explained on the last slide. That means there is nothing that we have unspecified in these E1 and E0 values, which are fitness values of these respective strategies except the alpha values. What have we achieved by this kind of description? First of all, we have an analytical model that we can investigate in order to look for the critical parameters that allow us to see the outbreak of co-operation. And secondly, we have specified everything except these nonlinearities that refer to the social herding process. Before I present the results, let me remind you on two limiting cases here. One limiting case is the theta equals zero, then the agents are only strategic, making only strategic decisions. They compare to payoffs, what's my payoff if I'm cooperating, what's my payoff if I would defect, and then they choose what gives them the higher payoff. We go back to our mean-field equation. We can calculate E1 and E0 that are the fitness values of these two strategies. In this case, it's very simple. We can predict that the whole thing dies out. That means there will be no co-operators because defection is the only evolutionary stable strategy. That is not new. This is known for the PD game all the time. Therefore, we use this case as a reference case. Now let us later include social herding, and let's try to get away from this result, which is our reference point, and what we get without social herding. Before, let me mention the other limiting case, namely where the theta is equal to one. That means there is no strategic behavior at all. There's only simple social herding behavior, and then we are back at what Maxi just described as a linear voter model, or it's a class of voter models in general. We are particularly interested in positive frequency dependence. Remember, we are talking about alpha naught, alpha 1, and alpha 2. If we order them like this, this is called positive frequency dependence. Alpha naught describes my response if no co-operator is in my neighborhood. Alpha 1 describes my response if one fourth of co-operators is in the neighborhood. Alpha 2 describes if two fourths, one half of co-operators is in my neighborhood, and so forth, right? This is the meaning of it. The special case of the linear voter model I just mentioned here, so we will use this all as a reference case. Why is this important? Because we know from the linear voter model that the population, at least for this mean field approach, will always convert to one strategy. It can be either defection or co-operation, but it will always converge. If I run the game a 1000 times, then I see 50% end up with co-operation, 50% end up with defection. But for an individual run, I always get either defection or co-operation. And now I'm thinking of these nonlinear values that I can choose for the alpha 1. If you look here in this little phase diagram, alpha 0 is set to 0, so we are just talking about alpha 1, alpha 2. That is the point of the linear voter model. Alpha 1 is one fourth, alpha 2 is two fourths or one half, right? So here we have the area of positive frequency dependence, and here we have other areas. The interesting one is the yellow area. I can choose alpha 2 values that it looks a bit like this, against the trend. This is a linear voter model where there is a direct proportionality between the frequency of agents playing a particular strategy and my choice of that particular strategy. But against the trend, it's different. If this is a minority, then I choose the strategy, but if it becomes a majority, then I switch to the other. Now, having said all this and the theoretical consideration, let us discuss what we can learn about the optimal design. We start with the naive approach, what you would usually do when you want to combine strategic behavior and social herding. You take the simple PD game, prisoner's dilemma game that I have described, and combine it with the linear voter model. So I run a little simulation here. Claudia was kind enough to prepare this applet for us. Alpha 1 is point 1, it's one fourth, and this is one half. So you see that's the linear voter model, right? The theta that describes how much is this herding important, it's set to a quite high value, point 9. Why did I do that? Because I already know if the theta is very low, in particular if the theta is zero, then I always end up with defection. So I do not need to pay special attention to that case, that's my reference case. I try to find out what happens if the theta is very different from zero. And then I have the initial condition that gives me the initial fraction of cooperators and defectors. I already had the cooperators a bit, so I could have started with point 5, but let us take this. So now we go through this step by step. So blue means cooperators, yellow means defectors. That's a spatial game, but for the mean field limit it looks the same. Now these agents interact with each other in the same way I have described. Some of them follow a herding, a local herding. Others follow a strategic decision by just adopting the strategy with the highest payoff. Okay, what you see here is that there are clusters of co-operators, but these clusters in the long run die out. And if I let it run to the very end, so then it looks like this. What's the conclusion of this? The conclusion is that the linear-voter model does not help us at all in boosting cooperation. Why is this? I mean, that's why we have the mean field equation. For we look this up and then we see that the terms that contribute to social herdings from the linear-voter model just cancel each other out. So I'm not surprised that the linear-voter model does not lead to anything. But that's at least something we should start with. Second case is now we try to use deviations from the linear-voter model. And I'll refer again to this little diagram. That was the linear-voter model and now my idea is now to fix the alpha one and just play around with values of the alpha two. That's what I do. I could choose any variant of the alpha one and the alpha two, but for reasons that will become obvious other than the next point, we just want to vary the alpha two. The red line here is the linear-voter model. That means the alphas are directly proportional to the frequency of co-operators. And these colored lines are deviations either below or above this point. Particular, please understand, I just vary the alpha two. Who's aware of what the alpha two is doing in this model? The alpha two applies if the frequency is one-half. I'm an agent and I'm surrounded by half of co-operators and half of defectors. And I have to decide what to do. I can calculate the payoff, but if I want to follow the herding, then I have a problem because both of them co-operators and defectors are represented by the same fraction. So what the alpha two is doing, it breaks the symmetry either into this or the other direction. That's a very important point. So let me maybe first run a simulation here. We lower this a bit to not help the co-operators too much. We leave the c-tub as 0.7 and here we go to a high value like 0.8 for example. So now we... that was too fast, but anyway. You see, even that I started with a very low initial fraction of co-operators, thanks to this herding effect and thanks to the non-linear r-e-t in the response to this fraction, I get a state where the majority is co-operating. So we have systematically investigated this in this phase diagram. Here you see alpha one and alpha two and the color code gives you the fraction of co-operators in the system. That means yellow is no co-operator, there are only defectors. Note the linear r-voter point. We have already seen that our game leads to only defection in the linear r-voter. But there is a very interesting error here where it is deep blue and this means there is a vast majority of co-operators. And of course we can tune this a bit in order to come to a very close to 90 or 100%. There are three important messages from this phase diagram. The first one, a poor positive frequency dependence does not lead to success. If you want to design a mechanism then more is better in terms of frequency dependence does not help you. The more agents play that and that strategy, the more I am inclined to order use the strategy does not help you. That's the first important thing. The second thing is here if we go back for this, the purple one is the most important curve here. Here this is positive LA effect. The positive LA effect means in non-monotoners dependence on the frequency. And this applies only for one particular large transition probability namely for this alpha two, which is important to break the time. This is nice because you see I could have chosen other combinations of alpha one and alpha two in order to get something blue in the area here. But it is more efficient to just concentrate on the time. Let's assume I wanted to tune alpha one. What's alpha one? Alpha one is my behavior if 25% of the community is collaborating. If you want to get me to also collaborate if only 25% of the community is collaborating and 75 not, then you have to do a lot of effort to convince me to become a co-operator at that stage. That means tuning alpha one or alpha three respectively makes a lot more effort in pushing a society towards cooperation. But by just looking into alpha two, which is a tie situation, then we have a very efficient way of tuning the system behavior. This shows us what's the role of the social herding. Remember this variable theta decides how much I'm influenced or prone by social herding. You see if the theta is below 0.7, nothing happens. This always ends up in defect. That means it's very important to have social herding, otherwise you don't get above this limit. The second thing is if you look here, these different curves are different values of alpha two color coded here. We see that of course the curve depends on the value here, but not as much as it depends on the theta. That's important. The third message that we see here, we get a steep increase of the number of the fraction of co-operators in the system. That means everything between 0.6 and 0.8 is reasonable here. But in order to get 100% of co-operators, we need to go to the real social herding without any strategic behavior. Why is this the case? Because if you have a state with only co-operators, then it's a very attractive for agents to switch to defection. Because then they get a full payoff from exploiting the co-operators. And therefore we get this, the full co-operation only if we completely ignore the strategic behavior. But still if we do not completely ignore, we have a majority of agents playing this. With this I come to one extension in the last few minutes that are left. It's about migration. Let's assume now that instead of the prisoner-style lemma game, we have an iterated prisoner-style lemma game. That means we have a repeated strategic interaction. Then we can distinguish between these different strategies. TFT and all C are co-operative strategies and all D and anti-TFT are defective strategies. This is simply, there's a four out of eight possible strategies and they are possible in this society. We are interested in the outbreak of co-operation. And we assume that there is a payoff dependent reproduction. It's a bit similar to what we have used before, but it's not the same. Here the underlying equation is a replicator dynamics and the other one was a logic function. There are differences. That means if I have a successful strategy, this successful strategy will reproduce more than a not successful strategy. And now we introduce a new term here that is migration. I call this unconditional migration because there are papers about success-driven migration. Success-driven migration means I buy somehow in the success of the model. Therefore we assume that there is no relation to success, but just a simple herding. A herding means one someone migrates and 10% of the population follows this person without calculating if it's good or bad for me. That's the idea. Unconditional. What are the results? Here we have three of these countries or islands and you see this FSC initial fraction of TFT. It's very low. 10%, 18%, 30%. And then they have this case where we have no migration and then we see only in one island TFT survives as a strategy. This is because the threshold is something point two. And in all the other islands this cooperative strategy dies off. But already with a very small migration rate, that means with this very small unconditional social herding, we can tune all these islands into cooperative islands. We import only a few agents playing TFT and get in turn lots of agents that are defective because remember this is an unconditional migration. No one really calculates payoffs. And still we get this kind of behavior. On the last slide, I show you that this does not work for all values of the migration which is M is basically a measure of the social herding. It's a migration rate that's a measure of the social herding. Here you see without migration you have only two islands in the five island models that preserve cooperation. If you increase this, then you get all the five islands to cooperation which you have the optimal social herding. And if you further increase the herding, then you destroy the whole effort. That's a very important thing. With this I come to my conclusions. I'd like to convey four different messages. We have introduced social herding in addition to a strategic behavior to avoid the lock-in in suboptimal states. And we have shown that social herding allows us a transition to cooperation because of social influence and not because of payoff considerations. The second important point is social herding uses less information than for example strategic behavior because there is no payoff calculation, no comparison of alternatives, no strategic decision. There's simple imitation. The social herding as I have shown in this result, matters most in this tie situation. That is where we had this LA effect that means the non-monotonal behavior of the frequency dependent. And by focusing just on the tie situation we have a very cost efficient way of influencing the system because we do not need to care about all the other constellations that are possible. And eventually I have also shortly discussed a special form of social herding that is unconditional migration. And I could show that there is an optimal migration rate. That means an optimal rate of social herding to transform a defecting population into a population of cooperators. With this I would thank you for your attention. And the most important slide is probably this one. And there are also a few flyers outside. And if you want to register just for you we still keep the registration side open. Thank you very much. Thank you very much. Fine. Okay, there's the first question up there. Can somebody help with microphones? Otherwise it keeps me fit. Been running for a long time. Yeah, it's about this multinomial probability that you have in your model. There's a parameter which is beta. And I missed, maybe it's my fault, I missed the role of this beta. Because based on what I know, this discrete choice model, beta is this intensity of joy. Okay. So it may be important. Okay, it is important. So first of all what I have shown in this logic function is the most general case of writing up these influence, the strategic and the herding influence. Right? So we didn't use it this way. Instead we used the deterministic limit of this. So which is basically the worst case scenario. Everyone knows that random fluctuations always help cooperation to break through, therefore we dropped this to really look into the worst case scenario where there are no random fluctuations to give a chance to cooperation. So, but in the most general case we can use these and can also play with the randomness in the decision process. Any other comments or questions? Yes. Your approach does not seem to need lack of information. It's just kind of confirmation to norm, for example. Yeah, I don't care how you name social herding. It can be confirmation to a norm if you want to interpret this like this. Of course, that's clear. The important thing is that by including the social herding you do not have any calculation of payoff. You do not need to know all the alternatives. You simply follow what the majority in your neighborhood is doing. That's the important thing. So actually it's less information, but of course you can interpret this as an addition to a social norm. Yes. I don't see a further question, but I have one actually. Certainly learning how to promote cooperation can be quite useful in many contexts. When it comes to overcome text evasion or global warming or overfishing or other problems actually. But we know that some people know how to create such a trend towards cooperation and can create a mass psychology somehow. We've seen instances in history where that ended very badly. So as we learn how to foster cooperation through mechanisms, aren't there any dangers that could come up and how to handle this, that this is kind of a two-sided double-edged sword somehow? I mean, what about tea parties? Are they a good invention or a bad invention for democracy? It's not so clear to me. And there's maybe no obvious answer, but maybe you have some thoughts on that. Okay. Yes, you are right. I mean, if you want to interpret these results, then you see I played a lot this card of the uninformed individual. Actually, we are just running simulation where part of the agents are informed. That means they are able to play strategic games. And the other part just look into these informed agents. So if you want to transfer this in a real situation, then of course who wants to be the uninformed person? We all want to be the ones with the full information. That means to suggest really this to people and say, be happy that you do not know all your alternatives. That's a very difficult thing to convey. And the second remark is also important. The success of these models are based on the fact that you have a non-monotonal frequency dependent. That means in terms of in society, people drop out early enough to not reinforce a trend too much. That's also something that is very difficult to implement in a real society. Because we have to somehow control this positive herding effect by means of this alating. What is the right value of reducing the response if everyone wants to do just the same? If you go for policy design, these are two critical points that of course limit the easy transfer into a real situation. Alright, thank you very much, Frank.
 And with this I would like to welcome Frank Schweitzer, who is of ETH Zurich.  Now he is the Office of Physicists as well, but now he is very serious about economics.  And he is a big team trying to focus on network aspects and dynamic aspects,  non-equilibrium models in economics.  And also on large-scale data mining has come up with a number of very interesting  and innovative publications in the past years.  And actually there is another workshop that I'd like to mention, which is Economics on the Move.  And I'm pretty sure that would be interesting for you as well, so feel happy to try.  Thank you very much, Frank. Are you ready to go?  Yeah, okay. Good afternoon, everyone.  It's my great pleasure to present some work from the Chair of Systems Design.  Actually our research is mostly concerned with what we call data-driven modeling.  We are interested in big data, as Dirk just said.  But I opted out to talk about this for reasons.  The first one I don't dare to compare and compete myself with these people here, like Alex Vespignani.  The second thing, I personally get bored to always talk about cyber emotions and these kind of things.  The third reason I thought for a workshop on agent-based modeling,  it would be appropriate to present an agent-based model that can be also served analytically.  And fourth, I thought for a workshop, it would be appropriate to present some work in progress.  And that's what we do now.  The question is, can we design social hurting to enhance cooperation?  The take-home message is yes.  And there are at least three different approaches that we are following in these three different papers.  Two of these I will shortly discuss today.  And the third one is probably mentioned tomorrow by Hans Söntzers.  But of course, I wouldn't have suggested this topic if we were not able to enhance cooperation by means of social hurting.  The question is, then, what's the problem in detail,  although what's the model that we have chosen to describe the problem,  what is the optimal design to enhance cooperation and the fewer extensions?  So let me go first into the problem.  Social hurting and cooperation are not that different.  As you can, for example, see in this little picture here, there are lots of communalities.  I mean, some of you might be able to see what this actually is.  Now we see it a bit better, right?  So, okay.  So both social hurting and cooperation have in common that individual decisions are made based on the observed or the assumed actions of others.  There is the example of buying a product because you observe someone else is buying the product.  You don't know about the reasons, of course, but you might also guess about the reasons.  There are other examples here.  But more important are the differences.  Social hurting basically describes a very simple imitation process,  all of what we call contagious behavior.  That means an agent I copies the action of another agent J without knowing the consequences.  That's a very important thing.  So the assumption for social hurting is there is no information available on the side of I,  but maybe J has all the information about choosing this product and therefore I simply copies the decision of J.  And this, of course, implies that I and J are somehow similar.  They have some profile features in common or they have similar responses.  And then it also makes sense to copy decisions or actions of others because this reduces your own risk of making the wrong decision.  Cooperation, on the other hand, is a very different behavior because it's based on a strategic decision to maximize the payoff.  That means I, agent I, chooses the action that I wants to do based on what J is doing in response to J.  And the action is chosen in such a way that the payoff is maximized.  The assumption here is differently.  The assumption is that there is full information on the side of I.  I knows all the alternatives.  I is able to calculate every payoff correctly and then I can compare both payoffs or all the payoffs.  And this, of course, is based on the assumption as well that the payoffs can be calculated.  And you can think of very many situations.  Think of the picture I have just shown where you have difficulties to calculate the payoff for yourself, right?  But the intuition, if you compare social hurting and strategic behavior, is it's always better to have more information.  If you are able to choose among all the alternatives and you know all the outcome, you reduce your own risk of making the wrong decision, choosing the wrong action.  And therefore, it's much better if you have the full information available.  That's at least what we think intuitively.  But more is not always better and that's also true for the available information.  I want to present two counter examples to just give you a flavor of where information and in particular more information,  hemp-ass finding the better solution.  In the first example, we referred to the phenomenon of the wisdom of crowds.  We did experiments with humans together with Sturck and published in this paper here.  We also developed an agent-based model.  The situation was the following.  Individuals had to make a guess on an arbitrary question, how long is it, what's the length of the border of Switzerland, for example.  And then they had to do this in five rounds and they were treated with three different information regimes.  In the first case, they had no information available about the guesses of other people.  In the second case, they had the aggregated information available about the guesses of others, so what's the mean value of all the guesses.  And in the third case, they had all the trajectories available of how the others have guessed the length of the border of Switzerland  and how they have adjusted their values.  And then individuals got to respond to this.  It's perfectly fine if you cannot read the numbers in this picture.  The most important thing is here in this little bar on the bottom.  If we use a measure for the quality of the guess, the wisdom of crowd indicators,  and we see that the wisdom of crowd indicator severely declines the more information we give to the humans.  That means the prediction usually becomes less accurate if people have more information available about the guesses of others.  And the case that makes it even worse is if you ask people about this,  then they are convinced that the wrong results they converge to actually is a better one  because they saw each other converging to something.  That means this is a real tricky threat in this kind of phenomenon.  Everyone converges to the wrong result and at the same time, we are all convinced that we have converged to the right result.  There are two important mistakes involved in this presentation of more information.  The second example comes also from a theoretical model where we try to describe network formation in an agent-based model.  These agents are described by utility and they had to create links.  There are two different scenarios here.  One is called incremental improvement.  The other one, best response.  In an incremental improvement, agent i tests if the utility will increase and agent j tests if the utility will increase.  And if both of these utilities increase, they decide to form a link.  In the best response case, agent i says, well, of course, the utility increased,  but maybe it will increase more if I link to another agent.  So every agent systematically checks all other agents in the system to find out what is the most optimal agent to create a link to.  It means in best response case, you have all the information available.  What you see here is the more information you have available, the worse the performance of the system is.  We know and can also verify this by mathematical proof that the optimal network looks like this,  more or less a fully connected network among the agent.  That's incremental improvement.  That's best response.  You see that the structures we reach are very different from the real, from the known optimal state.  That means the system gets trapped in a suboptimal state,  and because agents are always pointed back because of all this information to this suboptimal state, the system is never able to leave.  These are two examples where we see more information may not enhance the situation.  Then, of course, our hypothesis is maybe less information is a better one.  We use this as a hypothesis because we assume that less information may avoid the stateloc situation that I have just described,  or this log in in a suboptimal state.  In particular, we want to explore one important idea here, namely that we want to overcome a social dilemma  by including social hurting to a behavior that is usually assumed as strategic behavior.  This is a little graph I usually use to explain the situation.  I learned that no one really understands this, so it doesn't matter if we are very short about this.  Look at this dimension and let's assume that this axis measures the effort.  This is the strategic dimension, for example, of calculating the payoff.  We are here in the beginning of the state, so we might find a better state where negative means better, less effort, or even again.  We have to overcome a series of suboptimal states along this way.  If we instead include these other dimensions, then we might be able to find a detour that is, of course, longer,  but maybe avoids climbing up this mountain of suboptimal states.  At the end, because we go along this line, we end up in the same valley of positive of optimal states,  but not going this way, but that way.  We are trying to explore different mechanisms of getting into this direction.  Most notably, I'd like to point out that we do a lot of work on emotional influence.  Emotional influence is a specific representation of the social dimension here.  I'm not going to talk about this, as I said in the beginning.  Now, having said this as a motivation, what is the model we have used to describe this?  Sorry for the many equations here.  What we would like to do is we want to combine the social dimension, which is the social hurting,  and the strategic dimension.  We use a model of heterogeneous agent where each agent is described by two individual variables.  This theta describes a strategy, whether the agent defects or whether it co-operates.  Theta equals one means the agent co-operates.  The second variable, theta, describes to what extent is the agent prone to social influence.  So letter one is a continuous variable between zero and one.  With respect to the strategic interaction, we assume that there is a number of simultaneous two-person games,  and the payoff is described by this payoff matrix.  There are these two strategies of agent i, and there are the two possible strategies of agent j,  and then dependent of what i and j choose, you see these payoffs here.  For the numbers, we use the so-called prisoner-stile lemma game, where the payoffs are ranked according to these inequalities.  The important thing to notice is that t is the highest, like five, but two r is more than t plus s.  That means if two agents decide to co-operate, this accumulative payoff is larger than if one agent decides to co-operate,  and the other one decides to defect.  But if you see it from the perspective of the individual agent, defection is always the best strategy,  because you get then five points if you meet a co-operator, and you get at least one if you meet a defector.  So then based on this, we can now assume that n simultaneous games are played,  and the payoff of the agent depends, of course, on its own strategy and on the number of co-operators  and the number of defectors that he has met in these n independent games.  So this is simply the straightforward expression of the payoff,  dependent on whether I'm co-operating, then I get this, or whether I'm defecting, then I get this.  So if we scale it here by n, then we get this, and the little f here is the local frequency of co-operators.  That is going to be the important key variable here.  Every agent is described with the neighborhood and interacts with other agents in its neighborhood,  and the frequency of co-operators is the most important variable here.  The payoff values are fixed.  Now I have to include the social part into this,  and this is done when agents are able to update their strategies.  We have to talk about this transition rate.  You read it as all the other equations, always from right to left.  So the agent is in a state 1 minus theta,  and it has to decide whether it switches to the opposite state, which is theta.  And this depends on the number of co-operators in the neighborhood,  and it also depends on how much the agent is prone to social influence.  In order to combine this, we just have these two expressions here.  You see, g represents a strategic component which is based on the payoff,  whereas the f represents a social component which just results from the social hurting effect.  And the theta combines the two.  The theta is 1, then we are talking about hurting effects only.  If the theta is 0, then we are talking about strategic considerations only.  The question now is, what do we assume for the g and the a?  I have given you here the equations.  I am not going to present all the details.  There are a few things you have to notice.  The first one, it looks like a logic function.  There is something in the exponent that is normalized.  What is in the exponent?  The payoff.  The normalized payoff that the agent gets.  What the agent is doing in the strategic case,  it compares the payoff that the agent gets by choosing strategy theta  with the payoff that the agent would get by choosing strategy 1 minus theta,  which is the opposite.  And then the agent probably follows that strategy that gives him the higher payoff.  If you develop these expressions here,  then you see that this is usually proportional to the difference in this payoff.  For the social hurting part, we also have chosen a logic,  logic function.  And if you develop this here, then you get that it is proportional to the  frequency of the guys doing the opposite of what am I doing.  I am playing strategy 1 minus theta,  then the other guys are playing strategy theta.  And if I see very many agents in my neighborhood that are playing the opposite  strategy, then because of the social hurting,  I am more inclined to adopt their strategy.  I do this only because I see that there are so many of these,  and not because I know they have all the high payoffs.  You understand?  It can be all that they have the low payoff, but I do not know this.  And here is a nonlinear function in front of this frequency,  which we are going to use later on.  So last slide with the nasty details.  It's simply to show you what are the parameters we want to tune at the very end.  We have chosen n equal to 4, because we also want to compare a mean field  limit with a simulation on the lattice.  That's why we took Q.  And we have abbreviated these transition rates that I have explained on the previous  side simply by these C and D values.  C naught means I am a co-operator and I switch to defection,  but in my neighborhood there are no co-operators.  And C3 means I am a co-operator and I am switching to defection,  but in my neighborhood there are 75% of co-operators.  And now of course I have to describe these C's, and for the D's it's the similar thing.  So as I have explained, each of these C's and D's transition rates  is composed of two of these terms here.  One term related to the strategic behavior and the other one related to the social hurting.  For the strategic behavior we just go back to slides where I have printed the payoff of the agent.  This is a straightforward expression of what is the payoff if I have three co-operators  in my neighborhood out of four and so on and so on.  The same is true for the D.  And for the hurting part, C and D, I have simply used these alpha values.  That means I did not specify them.  Of course I can assume later that it is directly proportional to the frequency here,  but I want to make use of all the non-linear functions,  therefore I specify it in this very abstract way.  So what are the only parameters on this slide that are not known?  Alpha 0, alpha 1 and alpha 2.  Well, everything else is determined by what we have in the game.  Last slide to wrap up with this.  If you specify it like this, then we are able to derive a mean-field equation  for the global frequency of co-operators.  This has a form of a fitness selection equation.  E1 is the fitness associated with the co-operators and E0 is the fitness associated with the defectors.  You see that of course the share of the co-operators increases  if the fitness of the co-operators is larger than the fitness of the defectors.  That is one thing that you get immediately out of the mean-field equation  and the E1 and the E0 are known to us because they are simply specific functions  of these C and D values that I have explained on the last slide.  That means there is nothing that we have unspecified in these E1 and E0 values,  which are fitness values of these respective strategies except the alpha values.  What have we achieved by this kind of description?  First of all, we have an analytical model that we can investigate  in order to look for the critical parameters that allow us to see the outbreak of co-operation.  And secondly, we have specified everything except these nonlinearities  that refer to the social herding process.  Before I present the results, let me remind you on two limiting cases here.  One limiting case is the theta equals zero,  then the agents are only strategic, making only strategic decisions.  They compare to payoffs, what's my payoff if I'm cooperating,  what's my payoff if I would defect, and then they choose what gives them the higher payoff.  We go back to our mean-field equation.  We can calculate E1 and E0 that are the fitness values of these two strategies.  In this case, it's very simple.  We can predict that the whole thing dies out.  That means there will be no co-operators  because defection is the only evolutionary stable strategy.  That is not new.  This is known for the PD game all the time.  Therefore, we use this case as a reference case.  Now let us later include social herding,  and let's try to get away from this result, which is our reference point,  and what we get without social herding.  Before, let me mention the other limiting case, namely where the theta is equal to one.  That means there is no strategic behavior at all.  There's only simple social herding behavior,  and then we are back at what Maxi just described as a linear voter model,  or it's a class of voter models in general.  We are particularly interested in positive frequency dependence.  Remember, we are talking about alpha naught, alpha 1, and alpha 2.  If we order them like this, this is called positive frequency dependence.  Alpha naught describes my response if no co-operator is in my neighborhood.  Alpha 1 describes my response if one fourth of co-operators is in the neighborhood.  Alpha 2 describes if two fourths, one half of co-operators is in my neighborhood,  and so forth, right?  This is the meaning of it.  The special case of the linear voter model I just mentioned here,  so we will use this all as a reference case.  Why is this important?  Because we know from the linear voter model that the population,  at least for this mean field approach, will always convert to one strategy.  It can be either defection or co-operation, but it will always converge.  If I run the game a 1000 times, then I see 50% end up with co-operation,  50% end up with defection.  But for an individual run, I always get either defection or co-operation.  And now I'm thinking of these nonlinear values that I can choose for the alpha 1.  If you look here in this little phase diagram, alpha 0 is set to 0,  so we are just talking about alpha 1, alpha 2.  That is the point of the linear voter model.  Alpha 1 is one fourth, alpha 2 is two fourths or one half, right?  So here we have the area of positive frequency dependence,  and here we have other areas.  The interesting one is the yellow area.  I can choose alpha 2 values that it looks a bit like this, against the trend.  This is a linear voter model where there is a direct proportionality  between the frequency of agents playing a particular strategy  and my choice of that particular strategy.  But against the trend, it's different.  If this is a minority, then I choose the strategy,  but if it becomes a majority, then I switch to the other.  Now, having said all this and the theoretical consideration,  let us discuss what we can learn about the optimal design.  We start with the naive approach, what you would usually do  when you want to combine strategic behavior and social herding.  You take the simple PD game, prisoner's dilemma game that I have described,  and combine it with the linear voter model.  So I run a little simulation here.  Claudia was kind enough to prepare this applet for us.  Alpha 1 is point 1, it's one fourth, and this is one half.  So you see that's the linear voter model, right?  The theta that describes how much is this herding important,  it's set to a quite high value, point 9.  Why did I do that?  Because I already know if the theta is very low,  in particular if the theta is zero, then I always end up with defection.  So I do not need to pay special attention to that case,  that's my reference case.  I try to find out what happens if the theta is very different from zero.  And then I have the initial condition that gives me the initial fraction  of cooperators and defectors.  I already had the cooperators a bit, so I could have started with point 5,  but let us take this.  So now we go through this step by step.  So blue means cooperators, yellow means defectors.  That's a spatial game, but for the mean field limit it looks the same.  Now these agents interact with each other in the same way I have described.  Some of them follow a herding, a local herding.  Others follow a strategic decision by just adopting the strategy with the highest payoff.  Okay, what you see here is that there are clusters of co-operators,  but these clusters in the long run die out.  And if I let it run to the very end, so then it looks like this.  What's the conclusion of this?  The conclusion is that the linear-voter model does not help us at all  in boosting cooperation.  Why is this?  I mean, that's why we have the mean field equation.  For we look this up and then we see that the terms that contribute to social herdings  from the linear-voter model just cancel each other out.  So I'm not surprised that the linear-voter model does not lead to anything.  But that's at least something we should start with.  Second case is now we try to use deviations from the linear-voter model.  And I'll refer again to this little diagram.  That was the linear-voter model and now my idea is now to fix the alpha one  and just play around with values of the alpha two.  That's what I do.  I could choose any variant of the alpha one and the alpha two,  but for reasons that will become obvious other than the next point,  we just want to vary the alpha two.  The red line here is the linear-voter model.  That means the alphas are directly proportional to the frequency of co-operators.  And these colored lines are deviations either below or above this point.  Particular, please understand, I just vary the alpha two.  Who's aware of what the alpha two is doing in this model?  The alpha two applies if the frequency is one-half.  I'm an agent and I'm surrounded by half of co-operators and half of defectors.  And I have to decide what to do.  I can calculate the payoff, but if I want to follow the herding,  then I have a problem because both of them co-operators and defectors  are represented by the same fraction.  So what the alpha two is doing, it breaks the symmetry  either into this or the other direction.  That's a very important point.  So let me maybe first run a simulation here.  We lower this a bit to not help the co-operators too much.  We leave the c-tub as 0.7 and here we go to a high value like 0.8 for example.  So now we... that was too fast, but anyway.  You see, even that I started with a very low initial fraction of co-operators,  thanks to this herding effect and thanks to the non-linear r-e-t  in the response to this fraction, I get a state where the majority is co-operating.  So we have systematically investigated this in this phase diagram.  Here you see alpha one and alpha two and the color code gives you the fraction  of co-operators in the system.  That means yellow is no co-operator, there are only defectors.  Note the linear r-voter point.  We have already seen that our game leads to only defection in the linear r-voter.  But there is a very interesting error here where it is deep blue  and this means there is a vast majority of co-operators.  And of course we can tune this a bit in order to come to a very close to 90 or 100%.  There are three important messages from this phase diagram.  The first one, a poor positive frequency dependence does not lead to success.  If you want to design a mechanism then more is better in terms of frequency dependence does not help you.  The more agents play that and that strategy, the more I am inclined to order use the strategy does not help you.  That's the first important thing.  The second thing is here if we go back for this, the purple one is the most important curve here.  Here this is positive LA effect.  The positive LA effect means in non-monotoners dependence on the frequency.  And this applies only for one particular large transition probability namely for this alpha two,  which is important to break the time.  This is nice because you see I could have chosen other combinations of alpha one and alpha two  in order to get something blue in the area here.  But it is more efficient to just concentrate on the time.  Let's assume I wanted to tune alpha one.  What's alpha one?  Alpha one is my behavior if 25% of the community is collaborating.  If you want to get me to also collaborate if only 25% of the community is collaborating and 75 not,  then you have to do a lot of effort to convince me to become a co-operator at that stage.  That means tuning alpha one or alpha three respectively makes a lot more effort in pushing a society towards cooperation.  But by just looking into alpha two, which is a tie situation, then we have a very efficient way of tuning the system behavior.  This shows us what's the role of the social herding.  Remember this variable theta decides how much I'm influenced or prone by social herding.  You see if the theta is below 0.7, nothing happens.  This always ends up in defect.  That means it's very important to have social herding, otherwise you don't get above this limit.  The second thing is if you look here, these different curves are different values of alpha two color coded here.  We see that of course the curve depends on the value here, but not as much as it depends on the theta.  That's important.  The third message that we see here, we get a steep increase of the number of the fraction of co-operators in the system.  That means everything between 0.6 and 0.8 is reasonable here.  But in order to get 100% of co-operators, we need to go to the real social herding without any strategic behavior.  Why is this the case?  Because if you have a state with only co-operators, then it's a very attractive for agents to switch to defection.  Because then they get a full payoff from exploiting the co-operators.  And therefore we get this, the full co-operation only if we completely ignore the strategic behavior.  But still if we do not completely ignore, we have a majority of agents playing this.  With this I come to one extension in the last few minutes that are left.  It's about migration.  Let's assume now that instead of the prisoner-style lemma game, we have an iterated prisoner-style lemma game.  That means we have a repeated strategic interaction.  Then we can distinguish between these different strategies.  TFT and all C are co-operative strategies and all D and anti-TFT are defective strategies.  This is simply, there's a four out of eight possible strategies and they are possible in this society.  We are interested in the outbreak of co-operation.  And we assume that there is a payoff dependent reproduction. It's a bit similar to what we have used before, but it's not the same.  Here the underlying equation is a replicator dynamics and the other one was a logic function.  There are differences.  That means if I have a successful strategy, this successful strategy will reproduce more than a not successful strategy.  And now we introduce a new term here that is migration.  I call this unconditional migration because there are papers about success-driven migration.  Success-driven migration means I buy somehow in the success of the model.  Therefore we assume that there is no relation to success, but just a simple herding.  A herding means one someone migrates and 10% of the population follows this person without calculating if it's good or bad for me.  That's the idea. Unconditional.  What are the results?  Here we have three of these countries or islands and you see this FSC initial fraction of TFT.  It's very low. 10%, 18%, 30%.  And then they have this case where we have no migration and then we see only in one island TFT survives as a strategy.  This is because the threshold is something point two.  And in all the other islands this cooperative strategy dies off.  But already with a very small migration rate, that means with this very small unconditional social herding, we can tune all these islands into cooperative islands.  We import only a few agents playing TFT and get in turn lots of agents that are defective because remember this is an unconditional migration.  No one really calculates payoffs.  And still we get this kind of behavior.  On the last slide, I show you that this does not work for all values of the migration which is M is basically a measure of the social herding.  It's a migration rate that's a measure of the social herding.  Here you see without migration you have only two islands in the five island models that preserve cooperation.  If you increase this, then you get all the five islands to cooperation which you have the optimal social herding.  And if you further increase the herding, then you destroy the whole effort.  That's a very important thing.  With this I come to my conclusions.  I'd like to convey four different messages.  We have introduced social herding in addition to a strategic behavior to avoid the lock-in in suboptimal states.  And we have shown that social herding allows us a transition to cooperation because of social influence and not because of payoff considerations.  The second important point is social herding uses less information than for example strategic behavior because there is no payoff calculation,  no comparison of alternatives, no strategic decision.  There's simple imitation.  The social herding as I have shown in this result, matters most in this tie situation.  That is where we had this LA effect that means the non-monotonal behavior of the frequency dependent.  And by focusing just on the tie situation we have a very cost efficient way of influencing the system  because we do not need to care about all the other constellations that are possible.  And eventually I have also shortly discussed a special form of social herding that is unconditional migration.  And I could show that there is an optimal migration rate.  That means an optimal rate of social herding to transform a defecting population into a population of cooperators.  With this I would thank you for your attention.  And the most important slide is probably this one.  And there are also a few flyers outside.  And if you want to register just for you we still keep the registration side open.  Thank you very much.  Thank you very much.  Fine.  Okay, there's the first question up there.  Can somebody help with microphones?  Otherwise it keeps me fit.  Been running for a long time.  Yeah, it's about this multinomial probability that you have in your model.  There's a parameter which is beta.  And I missed, maybe it's my fault, I missed the role of this beta.  Because based on what I know, this discrete choice model, beta is this intensity of joy.  Okay.  So it may be important.  Okay, it is important.  So first of all what I have shown in this logic function is the most general case of writing up these influence, the strategic and the herding influence.  Right?  So we didn't use it this way.  Instead we used the deterministic limit of this.  So which is basically the worst case scenario.  Everyone knows that random fluctuations always help cooperation to break through, therefore we dropped this to really look into the worst case scenario where there are no random fluctuations to give a chance to cooperation.  So, but in the most general case we can use these and can also play with the randomness in the decision process.  Any other comments or questions?  Yes.  Your approach does not seem to need lack of information.  It's just kind of confirmation to norm, for example.  Yeah, I don't care how you name social herding.  It can be confirmation to a norm if you want to interpret this like this.  Of course, that's clear.  The important thing is that by including the social herding you do not have any calculation of payoff.  You do not need to know all the alternatives.  You simply follow what the majority in your neighborhood is doing.  That's the important thing.  So actually it's less information, but of course you can interpret this as an addition to a social norm.  Yes.  I don't see a further question, but I have one actually.  Certainly learning how to promote cooperation can be quite useful in many contexts.  When it comes to overcome text evasion or global warming or overfishing or other problems actually.  But we know that some people know how to create such a trend towards cooperation  and can create a mass psychology somehow.  We've seen instances in history where that ended very badly.  So as we learn how to foster cooperation through mechanisms,  aren't there any dangers that could come up and how to handle this,  that this is kind of a two-sided double-edged sword somehow?  I mean, what about tea parties?  Are they a good invention or a bad invention for democracy?  It's not so clear to me.  And there's maybe no obvious answer, but maybe you have some thoughts on that.  Okay.  Yes, you are right.  I mean, if you want to interpret these results,  then you see I played a lot this card of the uninformed individual.  Actually, we are just running simulation where part of the agents are informed.  That means they are able to play strategic games.  And the other part just look into these informed agents.  So if you want to transfer this in a real situation,  then of course who wants to be the uninformed person?  We all want to be the ones with the full information.  That means to suggest really this to people and say,  be happy that you do not know all your alternatives.  That's a very difficult thing to convey.  And the second remark is also important.  The success of these models are based on the fact that you have a non-monotonal frequency dependent.  That means in terms of in society, people drop out early enough to not reinforce a trend too much.  That's also something that is very difficult to implement in a real society.  Because we have to somehow control this positive herding effect by means of this alating.  What is the right value of reducing the response if everyone wants to do just the same?  If you go for policy design, these are two critical points that of course limit the easy transfer into a real situation.  Alright, thank you very much, Frank.
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