Evolution of consistent conjectures in semi-aggregative representation of games, with applications to public good games and contests - Alex Possajennikov (The University of Nottingham, Centre for Decision Research and Experimental Economics (CeDEx), 2016)
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.
Keywords: C72; H41; 330; semi-aggregative games; conjectural variations; evolutionary stability; public good games; contests