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Evolution of Consistent Conjectures in Semi-Aggregative Representation of Games, with Applications to Public Good Games and Contests

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  • Alex Possajennikov

    (School of Economics, University of Nottingham)

Abstract

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.

Suggested Citation

  • Alex Possajennikov, 2016. "Evolution of Consistent Conjectures in Semi-Aggregative Representation of Games, with Applications to Public Good Games and Contests," Discussion Papers 2016-08, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    • Handle: RePEc:not:notcdx:2016-08
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    References listed on IDEAS

    as
    1. Dixon, Huw D. & Somma, Ernesto, 2003. "The evolution of consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 51(4), pages 523-536, August.
    2. Possajennikov, Alex, 2009. "The evolutionary stability of constant consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 21-29, October.
    3. Cornes,Richard & Sandler,Todd, 1996. "The Theory of Externalities, Public Goods, and Club Goods," Cambridge Books, Cambridge University Press, number 9780521477185.
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    5. Costrell, Robert M., 1991. "Immiserizing growth with semi-public goods under consistent conjectures," Journal of Public Economics, Elsevier, vol. 45(3), pages 383-389, August.
    6. Richard Cornes & Roger Hartley, 2007. "Aggregative Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 201-219, April.
    7. Makowski, Louis, 1987. "Are 'Rational Conjectures' Rational?," Journal of Industrial Economics, Wiley Blackwell, vol. 36(1), pages 35-47, September.
    8. Jun–ichi Itaya & Makoto Okamura, 2003. "Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 5(1), pages 51-66, January.
    9. Possajennikov, Alex, 2015. "Conjectural variations in aggregative games: An evolutionary perspective," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 55-61.
    10. Sugden, Robert, 1985. "Consistent conjectures and voluntary contributions to public goods: why the conventional theory does not work," Journal of Public Economics, Elsevier, vol. 27(1), pages 117-124, June.
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    Keywords

    semi-aggregative games; conjectural variations; evolutionary stability; public good games; contests;
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