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The Set of Correlated Equilibria 2 x 2 Games

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  • Antoni Calvó-Armengol

Abstract

We develop a geometric procedure to get all correlated equilibria in a 2 x 2 game. With this procedure we can actually "see" all the correlated strategy profiles of a given game and compare it to the convex hull of the Nash equilibrium profiles. Games without dominant strategies fall into two different equivalence classes: (i) competitive games, that have a unique correlated equilibrium strategy, and (ii) coordination and anticoordination games, whose set of correlated equilibria is a polytope with five vertices for which we provide general closed-form expressions. In this latter case, there are either three or four vertices for the payoffs. In contrast, the convex hull of the Nash equilibrium strategies and payoffs always have three vertices.

Suggested Citation

  • Antoni Calvó-Armengol, 2003. "The Set of Correlated Equilibria 2 x 2 Games," Working Papers 79, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:79
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    Cited by:

    1. Iñarra García, María Elena & Laruelle, Annick & Zuazo Garín, Peio, 2012. "Games with perceptions," IKERLANAK 9099, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Saracho de la Torre, Ana Isabel, 2012. "The von Neumann-Morgenstern stable sets for 2x2 games," IKERLANAK 1576-1857, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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