

A Game-Theoretic Analysis of the Social Impact of Connected and Automated Vehicles

Ioannis Vasileios Chremos, Student Member, IEEE, Logan E. Beaver, Student Member, IEEE
Andreas A. Malikopoulos, Senior Member, IEEE
This research was supported in part by ARPAE’s NEXTCAR program under the award number DE-AR0000796 and by the Delaware Energy Institute (DEI).The authors are with the Department of Mechanical Engineering, University of Delaware, Newark, DE 19716 USA (emails: ;; .)

In this paper, we address the much-anticipated deployment of connected and automated vehicles (CAVs) in society by modeling and analyzing the social-mobility dilemma in a game-theoretic approach. We formulate this dilemma as a normal-form game by constructing an intuitive payoff function inspired by the socially beneficial outcomes of a mobility system consisting of CAVs. We show that the game is equivalent to the Prisoner’s dilemma which implies that the rational collective decision is the opposite of the socially optimum (e.g., Tragedy of the Commons). To tackle this phenomenon, we present two different approaches, i.e., one with a preference structure and the other with institutional arrangements. In the first approach, we implement a social mechanism that enforces players to non-CAV travel and derive a lower bound of players that leads to an equilibrium of non-CAV traveling. In the second approach, we investigate the possibility of players bargaining to create an institution that enforces non-CAV travel. We show that as the number of players increases, the incentive ratio of non-CAV travel over CAV-travel tends to zero. We also performed a numerical study for the institutional solution demonstrating the effectiveness of our results.

I Introduction

I-a Motivation

The reality of connected and automated vehicles (CAVs) is coming fast to realization [1]. Similarly with other past technologies, CAVs promise to be an incoming disruptive innovation with vast technological, commercial, and regulatory dimensions. Recently, there has been a significant amount of work on the technological or social impact of CAVs - such as safety, congestion, emissions, and energy consumption. CAVs will transform the transportation system of today and revolutionize our mobility system. On the other hand, one expected social consequence of CAVs is to completely reshape urban mobility in the sense of altered tendency-to-travel, and thus, highly increase demand in the transportation system. To elaborate on this point, evident from similar technological revolutions and human-social perspective have changed the way a technology is used and applied (e.g., the elevators’ impact on society [2]). Thus, we can most certainly expect that the deployment of CAVs in society will have unexpected outcomes, i.e., possible rebound effects (e.g., increased overall vehicle miles, decreased use of public transportation, higher demand for road usage, etc.) Although there have been numerous studies that provide qualitative analysis for the social impact [3, 4, 5], our game-theoretical approach aims to provide a formal analysis of the human decision-making regarding the expected social-mobility dilemma of the future travelers.

One may ask “Why we use Game Theory to analyze such a problem?” It is the authors’ belief that emerging transportation systems, e.g., CAVs, shared mobility, etc, will be characterized by their socio-economic complexity: (1) improved productivity and energy efficiency, (2) widespread accessibility, and (3) drastic urban redesign and evolved urban culture. This characteristic can naturally be modeled and analyzed using notions from Mathematical Psychology and Game Theory. One of the main arguments in this paper is that the social interaction of humans and CAVs can be modeled as a “social dilemma.” That is, we are only concerned with the impact of the human decision before the vehicle’s engine is even turned on. Informally, a social dilemma is any situation where there is a subtle yet unwanted discrepancy between individual and collective interest. From the early s, there was much development regarding social interactions and social dilemmas [6]. One of the most well-studied social dilemmas is Albert Tucker’s “Prisoner’s dilemma (PD) game,” formally introduced in in an attempt to describe general social dilemmas which occur in a variety of situations.

By considering a normal-form game of players, we acquire a significantly improved way to realistically model social dilemmas that occur in real-life, and most importantly, we obtain a multi-player structure that reflects G. Hardin’s “Tragedy of the Commons.” From its conception, the Tragedy of the Commons has been an important problem in economics and other fields as it describes a plethora of phenomena in which independent members of a society selfishly attempt to maximize their benefit of utilizing at least one common resource which is scarce. Thus, the individuals’ selfishness leads to the collective degradation of the society’s well-being. Noteworthy, even though the decision-makers are selfish and their decisions aim to maximize personal gain, they end up depleting the resource with unavoidable repercussions and losses [7]. In our context, the common resource is the road infrastructure shared by all the travelers, and the utilization is whether to travel with a CAV, or not. Intuitively, one can expect that if all travelers make the selfish decision to use a CAV for commuting, then congestion is unavoidable.

From the very beginning of the th century, A. Pigou argued that if a system’s decision-makers take autonomous decisions, then the resulting collective outcome most probably will be inefficient [8]. Social dilemmas have been extensively studied for systems that exhibit overpopulation, resource depletion, and pollution [9], while the PD game has been used to model vehicle congestion in a transportation network [10]. Inspired from notions of classical arguments on the theory of social contract, Okada [11] investigated whether cooperation might emerge in a social dilemma game with institutional arrangements. There have been attempts that model human behavior in social dilemmas with an emphasis on cooperation and with the goal to better explain the results of social psychology experiments [12]. Although the social effect of selfish-mobility behavior in routing networks of regular and autonomous vehicles has been studied [13], it seems that the problem of how CAVs will affect human tendency-to-travel and mobility frequency have not been adequately approached yet. On the other hand, analytical frameworks have been proposed to quantify and evaluate the impacts of CAVs from the technological perspective [14, 15]. Furthermore, coordination of CAVs at different traffic scenarios, e.g., intersections or vehicle-following, have been extensively evaluated in the literature [16, 17]. Recently, there has been research done on the rebound effects which might arise from the introduction of automation in a transportation system [18, 19]. For a detailed analysis of the effects of CAVs technologies on travel demand, see [20]. Recently, in the literature, it has been recognized that further research is required to identify and understand the potential impacts of emerging mobility [21, 22].

The contributions of this paper are:

  1. we provide a game-theoretic analysis of the conflict of interest and model the social-mobility dilemma as a social dilemma, and

  2. we apply two different in mindset mechanisms and approaches on how to prevent negative outcomes, e.g., similar to the Tragedy of the Commons outcomes.

Several research efforts reported in the literature have focused on studying social behavior regarding semi-autonomous driving and the selfish social decision-making of choosing a route to commute in a transportation network. Our analysis will complement these efforts by providing a framework that attempts to integrate the human social behavior in a mobility system consisting of CAVs. Moreover, our work in this paper expands the much-needed discussion on understanding the social impact and implications of CAVs by providing insights on how human behavior might react to an emerging mobility system. More specifically, our most important contribution is to rigorously show that without a well-thought intervention via regulations, or incentives, a society of selfish travelers will make the wrong collective decisions, and thus, we will end up with catastrophically sub-optimal performance of a such emerging mobility system.

The remaining of the paper proceeds as follows. In Section II, we provide a short overview of mathematical preliminaries for our analysis. In Section III, we present our formulation of the social decision-making regarding the CAVs as a normal-form game, and show that it is equivalent to a PD game. In Section IV, we introduce a preference structure to our game, and in Section V, we introduce a framework of institutions along with a numerical study of the results. Finally, we offer some concluding remarks, and discuss future work in Section VI.

Ii Mathematical Preliminaries

In this section, we present a brief overview of important notions in non-cooperative Game Theory (for reference see [23]). First, we assume that the players of the game are rational, in the sense that each player’s objective is to maximize the expected value of her own payoff. In addition, we assume that the players are intelligent, i.e., each player has full knowledge of the game and has the ability to make any inferences about the game that we, the designers, can make. In order to develop a rigorous framework that analyzes the social dilemma as a game, we need to formally define a few notions from Game Theory (e.g., game, dominant strategy, Nash equilibrium, and Pareto domination).

Definition 1.

A finite normal form game is a tuple , where

  • is a finite set of players with ;

  • , where is a finite set of actions available to player with being the action profile;

  • , where , is a real-valued utility function for player .

Definition 2.

Let be the strategy profile of player , be two strategies of player , and be the set of all strategy profiles of the remaining players. Then, (strictly) dominates if, for all , we have . A strategy is strictly dominant for a player if it (strictly) dominates any other strategy for that player.

Definition 3.

A player ’s best response to the strategy profile is the strategy such that for all . A strategy profile is a Nash equilibrium if, for each player , is a best response to .

In this paper, an “outcome” of a game is any strategy profile . Next, for completeness, we define the notion of Pareto domination. Intuitively, an outcome that Pareto dominates some other outcome improves the utility of at least one player without reducing the utility of any other.

Definition 4.

Let and . Then a strategy profile Pareto dominates strategy if, , for all , and there exists some for which .

Pareto domination is a useful notion to fully describe the social dilemma in a game. A Nash equilibrium may be Pareto-dominated by another outcome, yet Game Theory counter-intuitively predicts that it will not be played [24]. For further discussion of the notions in normal-form games, see [23]. Next, we provide our formulation and show that it is equivalent to the PD game.

Iii Game-Theoretical formulation

We consider a society of with , uncooperative players induced with a shared-resource which is open-access to all. We assume that the resource is limited, and since each player is rational, we expect them to behave selfishly towards the utilization of the resource. In our context, the common resource is the road infrastructure and players utilize the roads by traveling in a CAV, and thus, using the capacity of the roads.

Assumption 1.

We assume full CAV-penetration, and so each traveler/player may choose either to travel in a CAV or use another mode of transportation, e.g., train, walking or cycling, thereby not contributing to congestion.

In a game-theoretic context, each player has two possible actions, namely either for not traveling in a CAV (non-CAV travel) or for traveling in a CAV (CAV-travel). All players receive a benefit (utility) for deciding to commute in the society. For example, traveling using CAVs conveys benefits arising from flexibility, privacy, convenience, etc. So, if a player chooses to travel in a CAV, then they receive a benefit of , where with , and . However, traveling in a CAV is naturally the selfish choice as it exploits the society’s resource. Hence, for each player that decides to travel in a CAV, a cost of is imposed to the society as a whole and is paid out equally by all players, i.e., we define as the damage done to society.


In our formulation, we want to capture the potential consequence of the players’ decision to travel in a CAV. That means that using the capacity of the roads, and thus creating congestion, pollution, etc, will be represented by the cost and overall by the damage done to society.

We can write the final form of player’s payoff for traveling in a CAV as , and accordingly, player’s payoff for not traveling in a CAV as , where is the number of players who choose not to travel in a CAV other than player . Thus, we have the following payoff function:


To the end, for player , the benefit of traveling in a CAV is denoted by and the benefit of not traveling in a CAV by , where is the number of players who decide to non-CAV travel other than player . Note that the payoff of player depends not only on her own action but also on the number of the other non-CAV travelers.

At this point, we can formally formulate our game denoted by : we have which denotes the finite set of players with ; for each player the action set is , and , with is the payoff function of player . Thus, our game can be represented by the following tuple,


Next, we fully characterize game .

Lemma 1.

The payoff difference is positive and constant for all values and for all players . Furthermore, is monotonically increasing in .


We have and and so the difference is simply . Hence, is clearly positive by definition of and and also constant for all values . Furthermore, for ,


Subtracting (4) from (3) gives


which implies for all . Therefore, we conclude that is monotonically increasing in . ∎

To the end, we use to denote the payoff difference. We observe that the payoff difference, which can be interpreted as the non-CAV travel cost, increases as increases, and it is independent of how many players choose to travel in a CAV.

Lemma 2.

The benefit of CAV-traveling, , is increasing and concave. Furthermore, the total cost of non-CAV travel increases in .


Similarly as in Lemma 1, for ,


and so, . Since is an affine function, it follows trivially that it is concave. It is easy to see that increases in . ∎

Notice that Lemma 2 intuitively says that a player’s marginal benefit of traveling in a CAV is decreasing as the number of players increases.

Lemma 3.

The payoff function (1) is non-negative for all , i.e., for all . Furthermore, mutual non-CAV travel is preferred to mutual CAV-travel, i.e., is a Pareto relation.


Since and and as both benefits of non-CAV traveling and CAV-traveling are increasing in , the result follows. Also, by simple calculation, we have and which clearly leads to for all . ∎

Lemma 3 shows that game induces a Pareto relation, which implies that the equilibrium of mutual CAV traveling is Pareto-inferior to the alternative outcome which arises when all players choose to non-CAV travel. This is a signficant result since Pareto relations are directly associated with social dilemmas; something that we want to capture in our game.

A visualization of the payoff function (
Fig. 1: A visualization of the payoff function (1) evaluated using the values , , and . We notice that (by focusing on the red circle) with a certain number of non-CAV travelers the overall utility of non-CAV travel is greater than the utility of CAV-travel. This is the true meaning of a social dilemma in a CAV-transportation context.
Theorem 1.

The game defined in (2) is equivalent to the PD game, i.e., both games share an equivalent incentive structure.


By Lemma 1, we have for all which implies that the dominant strategy by rational players in the game is CAV-travel no matter how many players decide to non-CAV travel. By Lemma 3, the social dilemma induced structure is equivalent to that of the Prisoner’s dilemma. ∎

Corollary 1.

The game defined in (2) and the PD game provide equivalent incentives to the players, and thus, they result in equivalent outcomes.

Next, we show that interestingly by construction of the payoff function (1), non-CAV travel is more attractive from both the societal and the player’s perspective.

Proposition 1.

Consider the game defined in (2). By definition, the benefit of non-CAV traveling is and the cost of non-CAV travel is (i.e., the payoff difference). Then non-CAV travel is socially desirable:


and also individually desirable:


Both (8) and (9) can be easily verified by substitution of the corresponding functions in (1). ∎

Before we present the next result, we introduce the notation which gives the greatest integer that is less than .

Proposition 2.

Consider the game defined in (2). There exists a unique integer given by , such that


where is the minimum number of non-CAV travelers.


By substitution, we get the following equations:


We want to find a unique such that (10) holds. So, we have


which leads to


As is an integer, the last inequality (15) is true if and only if and is not an integer number. ∎

Proposition 2 intuitively implies that we need at least non-CAV travelers so that the benefit a player receives when they decide non-CAV travel will be greater than the dominant strategy (see in Fig. 1 the red circle).

Next, we seek a way to characterize an outcome of the game in terms of preference. Now, in most cases, identifying the “best” outcome is not possible, but there are certain situations that might be better from a societal standpoint.

Proposition 3.

The dominant strategy of universal CAV-travel, , is Pareto dominated by outcomes with .


We want to show that the outcomes with Pareto dominate the dominant strategy of universal CAV-travel. We only have to check two cases, namely and . For , we have


Let , where , so that


Subtracting from gives . Further for , note that is an increasing function in , thus which implies . Thus, for all players , , where . On the other hand, if , then for all players by the first inequality relation in Proposition 2. Hence, all outcomes which satisfy Pareto dominate the dominant strategy of universal CAV-travel. ∎

We note that by construction the payoff function (1) make non-CAV travel attractive but, as a consequence of Proposition 3, the decision to non-CAV travel is worthwhile to a player only if there are or more non-CAV travelers. Otherwise, everyone is no worse off at the dominant strategy of universal CAV-travel. This gives rise to the notion of the state of minimally effective non-CAV travel.

Definition 5.

The state of minimally effective non-CAV travel is the minimum number of non-CAV travelers, , such that an outcome Pareto dominates the universal CAV-travel equilibrium.

Clearly the state of minimally effective non-CAV travel is given by Propositions 2 and 3.

Next, we discuss two solution approaches applied in our game . Our goal is to derive conditions that ensure a coalition of non-CAV travel, which are at least as large as the minimum state of non-CAV travel.

Iv Nash equilibria and the population threshold

Iv-a Preference Structure

Usually, in Game Theory, we assume that players are only interested in their own payoff. One of our goals is to study, in a more realistic setting, the players’ social behavior, and so we impose to our game a “preference structure.”

A preference structure allows us to model a particularly interesting scenario: the rational players are interested not only on their own payoff but also on the relative payoff share they receive, i.e., how their standing compares to that of others [25]. The authors in [26] designed the “equity, reciprocity, and competition (ERC)” model which is a simple model capable of handling a large population of players with an “adjusted utility” function constructed on the premise that players are motivated by both their pecuniary payoff and their relative payoff standing. Notice that we changed our terminology of payoff function to adjusted utility function here. We do this to differentiate the difference between the absolute payoffs that players get from (1) and the adjusted payoffs players will get in a preference structure. One of the reasons we use the ERC model is because it has been successful in explaining the behavior of selfish players in social experiments than other standard modeling techniques.

Following [26], let the absolute payoff of player be given by from (1), and player ’s relative share of the payoff by , where is the total pecuniary payout. The adjusted utility function then is given by:


where and are the relative weights, and the ratio characterize the type of each player. Note that is differentiable, strictly increasing and concave, and is differentiable, concave, and has its maximum at . Let us discuss a simple example from [26].

Example 1.

We can explicitly define both and as:


where function expresses the standard preferences for the payoff functions (1); function describes in a precise way the collective importance of equal division of the payoffs (this is also called the “comparative effect.”) Consequently, the further the allocation moves from player receiving an equal share, the higher the loss from the comparative effect.

Iv-B Analysis for the Nash Equilibria and the Threshold of Non-CAV Travel

Our analysis in this subsection follows [25], but we apply it to our game defined in (2) along with the preference structure. Our goal is to study what influences strategic agents to non-CAV travel in our game .

We start our analysis by looking at the necessary and sufficient conditions for player to non-CAV travel, i.e.,


Equivalently, we have from [25] that , where


From (21), we can deduce that player will non-CAV travel if, and only if, there is overcompensation for the loss in absolute gain by moving closer to the average gain [25]. Hence, we can state the general conditions of a Nash equilibrium:


We now have a better understanding of how the number of other non-CAV travelers, and its value can make non-CAV traveling a rational strategy.

Lemma 4.

For a given distribution of ERC-types, is necessary but not sufficient to get a coalition size of where players free-ride. For a given payoff structure with , there exist ERC-types such that is an equilibrium coalition size.


If , it is impossible for a coalition to form in the game of size . On the other hand, if then condition (22) cannot hold for any player. However, the conditions for a Nash equilibrium given by (22) and (23) imply that if then there are types of players such that players non-CAV travel and players free-ride. ∎

Proposition 4.

By construction of the game together with the ERC preference structure, there always exists a Nash equilibrium of universal CAV-travel.

Proposition 4 follows directly from Lemma 4. We are though interested in finding a threshold of players that decide to non-CAV travel. The next proposition will help us do that.

Proposition 5.

The necessary condition for an equilibrium of non-CAV traveling is equivalent to


In order to obtain , it is necessary that by CAV-traveling, a player further deviates from the equal share than by non-CAV traveling, i.e.,


Rearranging and by eliminating the denominators, we get


Substituting the payoff functions from (1) and further simplification lead to


Simplifying (27) gives


We are now ready to prove the main result of the section.

Theorem 2.

For any given vector of types, a rational player chooses to non-CAV travel when at least half of the players non-CAV travel.


We only have to check on what conditions relation (24) is positive. By construction the payoff functions are nonnegative, and thus . In more detail,


which is clearly positive for all values of , and . Hence, the second component of (24) is positive for . Next, we look at the first component of (24). By substituting the payoff function from (1), we get


which is negative for all values of . We observe though is that the second component is much bigger and dominates the first component as long as . Hence, relation (24) is positive and we have for . Therefore, for any given vector of types, if a player cooperates at the equilibrium, then at least half of the players cooperate. ∎

The interpretation of Theorem 2 is that for any coalition to exist with size , a minimum of players must join. We showed that given the specific payoff structure of our game and along with the ERC preference structure, a coalition of non-CAV traveling could be formed provided that it is rather large. Thus, even if we impose a social mechanism that enforces non-CAV traveling in a society of players and satisfying (24), a coalition of at least size must be formed to create an equilibrium of non-CAV traveling. Therefore, the social mechanism will require significant influence over the players’ behaviors in order to create a state of effective non-CAV traveling. Though, this result is promising as it shows that a social solution can potentially prevent self-centered and destructive behavior towards the society.

V Creating an institutional arrangement

In this section, we take advantage of the equivalency of our game to the Prisoner’s Dilemma in order to use the non-cooperative game model of institutional arrangements framework of [11]. We prove in Theorem 3 that the ratio of non-CAV travel and CAV-travel in a deregulated society as the number of players increases, tends to zero. In other words, as the society becomes larger and larger, the incentive to cooperatively agree not to travel in a CAV tends to zero.

Players are free to create a social institution which binds them by selecting their actions. In other words, players agree to have an institutional arrangement with purpose to enforce an agreement of non-CAV travel. The first stage is the creation of a social institution, and this is done through participation negotiations, and thus the first stage is called “participation decision stage.” All players have to decide whether they will participate in negotiations for collective decision making, or not, without any knowledge of each others’ decisions. The outcome of the game at this first stage is either that some group of players is formed or not. All players decide to participate in negotiations or not based on their expectations about what will happen in the rest of the game. The possibility of non-CAV traveling is significantly affected by the number of players. That means that the outcome of the institutional arrangements depend on the players’ decisions in the first stage.


We emphasize that the above institutional arrangements framework is modeled as a non-cooperative game.

Our goal here is to investigate for our game the following question: does the number of players affect the possibility of non-CAV traveling?

The next proposition addresses the basic cases.

Proposition 6.

([11]) Let denote a player ’s decision to participate in bargaining for installing an enforcement agency; otherwise . When , the participation decision stage has a unique solution .

It is interesting enough that in the special case , both players agree to create an enforcement agency and also to non-CAV travel in the institutional arrangements. Next, we define an important ratio which will allows us to answer our question of interest.

Definition 6.

The incentive ratio of non-CAV travel and CAV-travel can be defined as a positive number given by:


In words, represents the ratio of players’ incentive to form the minimum group for non-CAV traveling, i.e., the group of non-CAV travelers, over their incentive to deviate unilaterally from the minimum group for non-CAV traveling. Given our game defined in , we have

Proposition 7.

([11]) The uncooperative solution of the institutional arrangements for our game prescribes the following player behavior:

  1. If , then all players participate in bargaining and they agree to non-CAV travel.

  2. If , then every player participates in bargaining with probability satisfying:

where and are given by Proposition 2 and (32), respectively.

We are ready now to prove our main result of this section which has to do about the limiting behavior of .

Theorem 3.

As the number of players increases, the incentive ratio of non-CAV travel and CAV-travel vanishes, i.e., tends to as tends to infinity.


Substitute into to get


By Proposition 2, is not an integer, thus we can write , where . Now taking the limit of as goes to infinity gives


or equivalently


We divide both numerator and denominator by and using the standard limit gives the result, i.e.,


Thus, we conclude that . ∎

To complement our understanding we performed a numerical study of the limiting behavior of , given in Table I. In the table, we have included the additional probabilities: shows the probability of some group of size or greater reaching an agreement, the probability of each player being an insider of some group with at least non-CAV travelers, and is the probability of each player being a free rider, i.e., existing outside of a group of at least non-CAV travelers.

3 3 0.930 1.000 1.000 1.000 0.000
4 3 0.166 0.333 0.111 0.086 0.025
5 4 0.253 0.503 0.192 0.160 0.032
6 5 0.302 0.602 0.236 0.204 0.031
7 5 0.066 0.139 0.001 0.001 0.000
8 6 0.129 0.269 0.006 0.005 0.001
9 7 0.175 0.363 0.014 0.011 0.003
10 7 0.037 0.078 0.000 0.000 0.000
11 8 0.083 0.174 0.000 0.000 0.000
12 9 0.120 0.252 0.000 0.000 0.000
13 9 0.023 0.048 0.000 0.000 0.000
14 10 0.059 0.124 0.000 0.000 0.000
15 11 0.089 0.188 0.000 0.000 0.000
20 14 0.034 0.072 0.000 0.000 0.000
25 17 0.002 0.004 0.000 0.000 0.000
30 21 0.033 0.070 0.000 0.000 0.000
35 24 0.011 0.023 0.000 0.000 0.000
40 28 0.033 0.069 0.000 0.000 0.000
45 31 0.016 0.033 0.000 0.000 0.000
50 34 0.002 0.004 0.000 0.000 0.000
60 41 0.007 0.015 0.000 0.000 0.000
TABLE I: Numerical study for game with the institutional arrangements where .
Plot of
Fig. 2: Plot of as a function of the number of CAV-travelers. The blue line shows the sequence of as increases from to .

From Theorem 3, the incentive ratio goes to zero as the number of players increases. In addition, from the numerical study summarized in Table I and Figure 2, the likelihood of bargaining for an institution, and probability of being an insider, approach zero as gets large. This implies that for large societies, the impact of self-realized non-CAV traveling is non-existent, and the universal CAV-travel strategy dominates. For small societies with there is certainty that players agree to bargain and create an institution for CAV-travel (which is not ideal).

Vi Conclusion

In this paper, we addressed the problem of the social consequences of decision-making of human interaction with connectivity and automation in a game-theoretic setting. We formulated the problem as a multi-player normal form game and showed that the incentive structure is equivalent to the Prisoner’s dilemma game. The proposed approach has the benefit of capturing the social dilemma which most likely will arise from the future social-mobility dilemma. We considered two different approaches, i.e., one was with a preference structure and the one with institutions. We investigated whether players will non-CAV travel and derived the conditions that guarantee non-CAV traveling in the game. In the first case, we came up with conditions for the Nash equilibrium and derived a threshold for non-CAV traveling; in the second case, we allowed players to create an institution that can enforce non-CAV traveling. We concluded that the incentive ratio of non-CAV travel over CAV-travel tends to zero as the number of players increases.

An interesting direction for future research should include a framework to analyze the impact of decision-making by relaxing the assumptions of complete information (e.g., inducing a Bayesian setting) that will aim at capturing the informational limitations of players in the game.


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