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.
Possajennikov, A. (2015). Conjectural variations in aggregative games: an evolutionary perspective. Mathematical Social Sciences, 77, https://doi.org/10.1016/j.mathsocsci.2015.07.003