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Games with perceptions

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  • Laruelle, Annick
  • Iñarra García, María Elena
  • Zuazo Garín, Peio

Abstract

We assume that 2 x 2 matrix games are publicly known and that players perceive a dichotomous characteristic on their opponents which defines two types for each player. In turn, each type has beliefs concerning her opponent's types, and payoffs are assumed to be type-independent. We analyze whether the mere possibility of different types playing different strategies generates discriminatory equilibria. Given a specific information structure we find that in equilibrium a player discriminates between her types if and only if her opponent does so. We also find that for dominant solvable 2x2 games no discriminatory equilibrium exists, while under different conditions of concordance between players' beliefs discrimination appears for coordination and for competitive games. A complete characterization of the set of Bayesian equilibria is provided.

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Paper provided by Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I in its series IKERLANAK with number Ikerlanak;2012-64.

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Date of creation: 23 Oct 2012
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Handle: RePEc:ehu:ikerla:9099

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Postal: Dpto. de Fundamentos del Análisis Económico I, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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Keywords: incomplete information; 2x2 matrix games;

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  1. Matthew Rabin., 1992. "Incorporating Fairness into Game Theory and Economics," Economics Working Papers 92-199, University of California at Berkeley.
  2. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
  3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  4. Antoni Calvó-Armengol, 2003. "The Set of Correlated Equilibria 2 x 2 Games," Working Papers 79, Barcelona Graduate School of Economics.
  5. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
  6. Eichberger, J. & Haller, H. & Milne, F., 1993. "Naive Bayesian learning in 2 x 2 matrix games," Journal of Economic Behavior & Organization, Elsevier, vol. 22(1), pages 69-90, September.
  7. Forges, Françoise & Vida, Péter, 2013. "Implementation of Communication Equilibria by Correlated Cheap Talk : the Two-Player Case," Economics Papers from University Paris Dauphine 123456789/8159, Paris Dauphine University.
  8. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  9. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
  10. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
  11. Kaneko, Mamoru & Matsui, Akihiko, 1999. " Inductive Game Theory: Discrimination and Prejudices," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 101-37.
  12. Bechara, Antoine & Damasio, Antonio R., 2005. "The somatic marker hypothesis: A neural theory of economic decision," Games and Economic Behavior, Elsevier, vol. 52(2), pages 336-372, August.
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