user2013: In Ouroboros, the more ADA you have the bigger the chance to get elected to mine the next block and get the rewards.
Apart from other parameters and up to the saturation level for a single poole this incentivizes high net worth entities to run several stake pools and/or to provide pledges.
At first sight this feels like it would incentivize centralization. I'm sure that's not the case but are there any papers about that? E.g. ones that simulate that via game theory?

user2013: After asking the great community in the Cardano Forum someone answered comprehensively and pointed me to a blog post with an abstract, a video and a link to the paper.

user4302: High net-worth individuals running multiple stake pools is not necessarily a problem, as long as:

the initial distribution of ADA is sufficiently decentralized (done)
the aforementioned individuals' share of ADA is not growing at an exponential rate (done)

The market is still young, in that the big BIG money hasn't entered yet. During times of high volatility (in either direction), trading volume spikes, and overall distribution of ADA increases.

On Pool Splitting and Pledge
There are several network parameters that influence stake flow/aggregation. k (saturation limit) might be the most well known, but it is not enough alone. When k is increased, saturated pools are incentivized to evenly split, so a0 comes in to counterbalance the splitting incentive with a consolidation incentive.
a0 governs how much of an impact pledge has on max pool rewards. When a0 is increased, higher pledge mean higher rewards, which incentivizes would-be pool splitters to keep more of their ADA in a single pool.
At the time of this writing, there is a linear relationship between a0 and max pool rewards, such that higher pledge ~ higher rewards. However, CIP-7 is in the process of being finalized and, once implemented, will modify the formula to have an n-root curve. This will balance out the

On Economies of Scale
In PoW, economies of scale pose a much greater centralizing force than in PoS. Let's imagine a single GPU retails for $1000. If an average consumer wanted to buy one or two GPU's, they'd have to pay full retail price. However, if there was some big time player with $1 million to spare, they'd likely get a better deal than the average consumer, and they'd buy each GPU at a lower-than-retail rate. In PoS this is not the case; if we leave aside market manipulation, there are no discounts given to big-time buyers of cryptocurrencies. One ADA is one ADA. 1M ADA is 1M ADA. Period.
Additionally, if for whatever reason a new coin comes along that is more profitable to mine (even in the short term) than the current most-profitable PoW coin, there would be a massive incentive for miners to switch over to mining the new coin, compromising the decentralization of the original network. In PoS, this is not the nearly the case. Charles said it best in one of his AMA's: would you rather have Roman mercenaries guarding Rome, or Roman citizens guarding Rome? Probably the latter.

Sorry, no papers here, just some humble pontification :)

user4382: If you compare the proof of stake concept to that of proof of work, you still  end up with the "more money you have the more blocks you get." The difference being POW you buy graphics cards versus buying Cardano for POS.
Parameter k is an important factor for decentralization in Cardano. Currently k is set to 500 which sets the cap of a saturated pool at 64 million Ada. I believe the plan is to move k to 1000 next which will make 32 million Ada the saturation point. Changing that parameter will contribute to decentralizing the network even more, but you are right, high net worth entities are just going to make even more pools, which does centralize the network. However, single pool operators currently make up the biggest pool group of the network, which is great for decentralization. (How many of them are using the same cloud providers is a different discussion)
Currently Binance is the worst for creating multiple pools. Since they can stake other people's Ada to their own pools (not allowing competition) they currently have 42 fully saturated pools. They are making around 45 blocks per Epoch per pool or ~1,890 blocks per epoch. There are ~21,600 blocks per epoch, this mean that Binance is controlling 8.75% of the network. This is a lot but can easily be cut back by encouraging people to move their Ada from exchanges.
Here is a blog post from IOHK that you might find interesting on parameters such as k.
I hope this is helpful!

2013: <p>In Ouroboros, the more ADA you have the bigger the chance to get elected to mine the next block and get the rewards.
Apart from other parameters and up to the saturation level for a single poole this incentivizes high net worth entities to run several stake pools and/or to provide pledges.
At first sight this feels like it would incentivize centralization. I'm sure that's not the case but are there any papers about that? E.g. ones that simulate that via game theory?</p>
 2013: <p><a href="https://forum.cardano.org/t/are-there-papers-e-g-game-theorie-based-on-how-ouroboros-encourages-decentralization-of-ada-among-its-users/88855/7" rel="nofollow noreferrer">After asking the great community in the Cardano Forum</a> someone answered comprehensively and pointed me to a <a href="https://blogs.ed.ac.uk/blockchain/2021/12/01/rethinking-information-technology-from-a-decentralisation-perspective-webinar/" rel="nofollow noreferrer">blog post with an abstract, a video and a link to the paper</a>.</p>
 4302: <p>High net-worth individuals running multiple stake pools is not necessarily a problem, as long as:</p>
<ul>
<li>the initial distribution of ADA is sufficiently decentralized (done)</li>
<li>the aforementioned individuals' share of ADA is not growing at an exponential rate (done)</li>
</ul>
<p>The market is still young, in that the big BIG money hasn't entered yet. During times of high volatility (in either direction), trading volume spikes, and overall distribution of ADA increases.</p>
<hr />
<h5>On Pool Splitting and Pledge</h5>
<p>There are several network parameters that influence stake flow/aggregation. k (saturation limit) might be the most well known, but it is not enough alone. When k is increased, saturated pools are incentivized to evenly split, so a0 comes in to counterbalance the splitting incentive with a consolidation incentive.</p>
<p>a0 governs how much of an <a href="https://docs.cardano.org/core-concepts/pledging-rewards" rel="nofollow noreferrer">impact pledge has on max pool rewards</a>. When a0 is increased, higher pledge mean higher rewards, which incentivizes would-be pool splitters to keep more of their ADA in a single pool.</p>
<p>At the time of this writing, there is a linear relationship between a0 and max pool rewards, such that higher pledge ~ higher rewards. However, <a href="https://cips.cardano.org/cips/cip7/" rel="nofollow noreferrer">CIP-7</a> is in the process of being finalized and, once implemented, will modify the formula to have an n-root curve. This will balance out the</p>
<hr />
<h5>On Economies of Scale</h5>
<p>In PoW, economies of scale pose a much greater centralizing force than in PoS. Let's imagine a single GPU retails for $1000. If an average consumer wanted to buy one or two GPU's, they'd have to pay full retail price. However, if there was some big time player with $1 million to spare, they'd likely get a better deal than the average consumer, and they'd buy each GPU at a lower-than-retail rate. In PoS this is not the case; if we leave aside market manipulation, there are no discounts given to big-time buyers of cryptocurrencies. One ADA is one ADA. 1M ADA is 1M ADA. Period.</p>
<p>Additionally, if for whatever reason a new coin comes along that is more profitable to mine (even in the short term) than the current most-profitable PoW coin, there would be a <strong>massive</strong> incentive for miners to switch over to mining the new coin, compromising the decentralization of the original network. In PoS, this is not the nearly the case. Charles said it best in one of his AMA's: <strong>would you rather have Roman mercenaries guarding Rome, or Roman citizens guarding Rome?</strong> Probably the latter.</p>
<hr />
<p>Sorry, no papers here, just some humble pontification :)</p>
 4382: <p>If you compare the proof of stake concept to that of proof of work, you still  end up with the &quot;more money you have the more blocks you get.&quot; The difference being POW you buy graphics cards versus buying Cardano for POS.</p>
<p>Parameter k is an important factor for decentralization in Cardano. Currently k is set to 500 which sets the cap of a saturated pool at 64 million Ada. I believe the plan is to move k to 1000 next which will make 32 million Ada the saturation point. Changing that parameter will contribute to decentralizing the network even more, but you are right, high net worth entities are just going to make even more pools, which does centralize the network. However, single pool operators currently make up the biggest pool group of the network, which is great for decentralization. (How many of them are using the same cloud providers is a different discussion)</p>
<p>Currently Binance is the worst for creating multiple pools. Since they can stake other people's Ada to their own pools (not allowing competition) they currently have 42 fully saturated pools. They are making around 45 blocks per Epoch per pool or ~1,890 blocks per epoch. There are ~21,600 blocks per epoch, this mean that Binance is controlling 8.75% of the network. This is a lot but can easily be cut back by encouraging people to move their Ada from exchanges.</p>
<p>Here is a blog post from IOHK that you might find interesting on <a href="https://iohk.io/en/blog/posts/2020/11/05/parameters-and-decentralization-the-way-ahead/" rel="nofollow noreferrer">parameters such as k.</a></p>
<p>I hope this is helpful!</p>
