Conjectural variations in aggregative games: An evolutionary perspective

• Evolutionary stability of conjectures in aggregative games is analyzed.
• In an infinite population, only consistent conjectures can be evolutionarily stable.
• In a finite population, only zero conjectures can be evolutionarily stable.
• Results are illustrated on linear-quadratic games that include Cournot oligopoly.

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.