Conjectural variations in aggregative games: an evolutionary perspective

Possajennikov, Alex

Abstract

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.

Citation

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

• Journal Article Type: Article
• Publication Date: Aug 6, 2015
• Deposit Date: Aug 7, 2015
• Publicly Available Date: Aug 7, 2015
• Journal: Mathematical Social Sciences
• Print ISSN: 0165-4896
• Electronic ISSN: 0165-4896
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 77
• DOI: https://doi.org/10.1016/j.mathsocsci.2015.07.003
• Keywords: conjectural variations, aggregative games, indirect evolution, evolutionary stability
• Public URL: https://nottingham-repository.worktribe.com/output/759434
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0165489615000670