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Game Theory and Applications in the Presence of Cognitive Limitations

Final Report Summary - GTAPCL (Game Theory and Applications in the Presence of Cognitive Limitations)

Full rationality assumes that agents know how the strategies of other economic agents depend on their private information and on the state of the economy. But, such knowledge is rarely accessible. There are various ways of introducing cognitive limitations. The analogy-based expectation equilibrium (Jehiel, 2005) assumes that players bundle the statistics from past play in different games or states of the economy in order to form their expectations. Thus, the expectations of agents are less fine than they are in the usual solution concepts used in economics, and it is of interest to analyze what the consequences of such coarse understanding are in classic economic environments.
Traditional models of reputation identify the idea of reputation with the idea of commitment. That is, assuming you would like to be confused with a type of player who always behaves in a given way (say refusing any deal that is not extremely favourable to you) the mere possibility that you really are this mechanical type allows you to credibly commit to behaving in the same way as this type. Yet, such a view does not capture the idea that you may be able to confuse those who look at your behaviour about which type you really are (because in the standard approach, no agent can be fooled). If however, those who observe you have a coarse understanding of your behaviour, you may be able to manipulate their beliefs, deceive them, and in turn take advantage of it. One may quantify how much can be gained in this case relative to the situation with fully rational observers, thereby offering a simple measure of the gain due to belief manipulation as opposed to the gains due to the commitment ability. This is most strikingly illustrated in zero-sum games in which there is no value to commitment and yet the approach shows that there is value to manipulation.
Another important application of the approach concerns the role of feedback in auctions. Typically, providing feedback about the bidding behaviour in past auctions plays no role in the classic approach given that in a Nash equilibrium agents have correct expectations. Yet, by playing on the feedback she provides, an auctioneer or auction house can typically influence how fresh bidders will process data from previous auctions to shape their expectations. As a result, bidders can be manipulated (which by the way calls for possible regulation regarding how feedback is framed to potential bidders). From a different (more positive perspective), one frequently observes absolute auctions, i.e. auctions with no reserve price in real life auctions. One also observes auctions with secret reserve prices, i.e. auctions with reserve prices that are unknown to the bidders. Absolute auctions are sometimes justified on the ground that they allow to attract more participation. Yet, when participants are fully rational, posting a reserve price below the seller’s valuation can never be justified. Similarly, it is hard to justify the use of secret reserve prices, even if these are sometimes informally viewed as providing a way not to frighten too much participants when one is willing to post a high reserve price. These auction formats can easily be explained though in environments in which buyers are not fully sophisticated in their understanding of how participation is affected by the choice of reserve price and how the reserve price is distributed when secret. An interesting by-product of the analysis is that there is no need to assume that buyers are completely irrational in their way of forming expectations to explain the use of such auction formats. It is enough that some buyers analyze past (participation and reserve price) data with sufficient coarseness to produce the desired conclusion that absolute auctions and auctions with secret reserve prices are natural auction formats to be expected in competitive environments. The analysis also permits to do welfare analysis that may be helpful to best manage the protection of buyers in auction houses.