Evolution of Consistent Conjectures in Semi-aggregative Representation of Games, with Applications to Public Good Games and Contests
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In a semi-aggregative representation of a game, the payoff of a player depends on a player’s own strategy and on a personalized aggregate of all players’ strategies. Suppose that each player has a conjecture about the reaction of the personalized aggregate to a change in the player’s own strategy. The players play an equilibrium given their conjectures, and evolution selects conjectures that lead to a higher payoff in such an equilibrium. Considering one player role, I show that for any conjectures of the other players, only conjectures that are consistent can be evolutionarily stable, where consistency means that the conjecture is, to a first approximation, correct at equilibrium. I illustrate this result in public good games and contests.
KeywordsEvolutionary Stability Public Good Game Interior Equilibrium Pure Public Good Strict Nash Equilibrium
I would like to thank Dirk Rübbelke and Wolfgang Buchholz for this opportunity. I would also like to thank Alex Dickson for inviting me to participate in April 2011 in a workshop on aggregative games, which incited me to think about conjectures and aggregative games, and develop the ideas leading to this paper. I also thank Maria Montero for improving the exposition in the paper.
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