CeDEx 2016-08: Evolution of Consistent Conjectures in Semi-Aggregative Representation of Games, with Applications to Public Good Games and Contests

Summary

In many economic games, players can have conjectures about how the other player react to changes, and adapt their own behaviour accordingly. For example, a firm's profit can depend on its own production level and the aggregate production of other firms, and a firm can expect other firms to adjust their aggregate production quickly if it changes its own output. The firm's decision how much it deems best to produce, and its actual profit, depend on its conjectures. What conjectures are sensible in such situations? Which ones can lead to better payoffs to a player and thus survive evolutionary pressure of selecting conjectures? And do such conjectures actually survive evolutionary pressure in some situations?

In this Nottingham School of Economics working paper, written for a volume in memory of former University of Nottingham professor Richard Cornes (to be published by Springer), Alex Possajennikov considers multiplayer games in which payoffs of a player can be represented to depend on a player's own choice and an aggregate measure of the other player choices (semi-aggregative representation). Players have conjectures about the changes in this aggregate measure and behave optimally given these conjectures. It turns out that only consistent conjectures, in the sense of correctly anticipating the marginal reaction of the aggregate measure, can be evolutionarily stable in general well-behaved games. It is shown that in some situations, such as public good games and contests, consistent conjectures are actually evolutionarily stable. The paper links the analysis to the works by Richard Cornes on conjectures of players in aggregative games and on public good games and contests.

CeDEx 2016-08, Evolution of Consistent Conjectures in Semi-Aggregative Representation of Games, with Applications to Public Good Games and Contests by Alex Possajennikov

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Authors

Alex Possajennikov

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