Conjectural variations in aggregative games: an evolutionary perspective
Possajennikov, Alex (2015) Conjectural variations in aggregative games: an evolutionary perspective. Mathematical Social Sciences, 77 . pp. 55-61. ISSN 0165-4896
Suppose that in symmetric aggregative games, in which payoffs depend only on a player's strategy and on an aggregate of all players' strategies, players have conjectures about the reaction of the aggregate to marginal changes in their strategy. The players play a conjectural variation equilibrium, which determines their fitness payoffs. The paper shows that only consistent conjectures can be evolutionarily stable in an infinite population, where a conjecture is consistent if it is equal to the marginal change in the aggregate determined by the actual best responses. In the finite population case, only zero conjectures representing aggregate-taking behavior can be evolutionarily stable.
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