Conjectural Variations in Aggregative Games: An Evolutionary Perspective
Suppose that in aggregative games, in which a player's payoff depends only on this player's strategy and on an aggregate of all players' strategies, the players are endowed with constant conjectures about the reaction of the aggregate to marginal changes in the player's strategy. The players play the equilibrium determined by their conjectures and equilibrium strategies determine the players' payoffs, which can be different for players with different conjectures. It is shown that with random matching in an infinite population, only consistent conjectures can be evolutionarily stable, where a conjecture is consistent if it is equal to the marginal change in the aggregate at equilibrium, determined by the players' actual best responses. In the finite population case in which relative payoffs matter, only zero conjectures representing aggregate-taking behavior can be evolutionarily stable. The results are illustrated with the examples of a linear-quadratic game (that includes a Cournot oligopoly) and a rent-seeking game.
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- Alex Possajennikov, 2003.
"Evolutionary foundations of aggregate-taking behavior,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 921-928, 06.
- Alex Possajennikov, 2001. "Evolutionary Foundations of Aggregate-Taking Behavior," Discussion Papers in Economics 01_10, University of Dortmund, Department of Economics.
- Müller, W. & Normann, H.T., 2005.
"Conjectural variations and evolutionary stability : A new rationale for consistency,"
Other publications TiSEM
a9dba38c-5ab2-4ec3-ba6f-2, Tilburg University, School of Economics and Management.
- Müller, W. & Normann, H.T., 2003. "Conjectural Variations and Evolutionary Stability : A New Rationale for Consistency," Discussion Paper 2003-44, Tilburg University, Center for Economic Research.
- Müller, W. & Normann, H.T., 2007.
"Conjectural variations and evolutionary stability in finite populations,"
Other publications TiSEM
b5bac987-362f-46e4-b478-c, Tilburg University, School of Economics and Management.
- Wieland Müller & Hans-Theo Normann, 2007. "Conjectural variations and evolutionary stability in finite populations," Journal of Evolutionary Economics, Springer, vol. 17(1), pages 53-61, February.
- Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, December.
- Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2004.
"What to Maximize if You Must,"
1414, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Chris Shannon, 2003. "What to Maximize if You Must," Theory workshop papers 658612000000000044, UCLA Department of Economics.
- Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2003. "What to Maximize If You Must," Game Theory and Information 0303002, EconWPA.
- HEIFETZ, Aviad & SHANNON, Chris & SPIEGEL, Yossi, 2003. "What to maximize if you must," CORE Discussion Papers 2003047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Morton I. Kamien & Nancy L. Schwartz, 1983. "Conjectural Variations," Canadian Journal of Economics, Canadian Economics Association, vol. 16(2), pages 191-211, May.
- Acemoglu, Daron & Jensen, Martin Kaae, 2013.
"Aggregate comparative statics,"
Games and Economic Behavior,
Elsevier, vol. 81(C), pages 27-49.
- Itaya, Jun-ichi & Dasgupta, Dipankar, 1995. "Dynamics, Consistent Conjectures, and Heterogeneous Agents in the Private Provision of Public Goods," Public Finance = Finances publiques, , vol. 50(3), pages 371-389.
- Martin K. Perry, 1982. "Oligopoly and Consistent Conjectural Variations," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 197-205, Spring.
- Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
- Dixon, Huw D. & Somma, Ernesto, 2003. "The evolution of consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 51(4), pages 523-536, August.
- Possajennikov, Alex, 2009.
"The evolutionary stability of constant consistent conjectures,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 72(1), pages 21-29, October.
- Alex Possajennikov, 2009. "The Evolutionary Stability of Constant Consistent Conjectures," Post-Print hal-00701872, HAL.
- Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
- Cornes, Richard & Hartley, Roger, 2012.
"Fully aggregative games,"
Elsevier, vol. 116(3), pages 631-633.
- Makowski, Louis, 1987. "Are 'Rational Conjectures' Rational?," Journal of Industrial Economics, Wiley Blackwell, vol. 36(1), pages 35-47, September.
- Bresnahan, Timothy F, 1981. "Duopoly Models with Consistent Conjectures," American Economic Review, American Economic Association, vol. 71(5), pages 934-945, December.
- Wieland Müller & Hans-Theo Normann, 2005. "Conjectural Variations and Evolutionary Stability: A Rationale for Consistency," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 161(3), pages 491-491, September.
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