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On Some Geometry and Equivalence Classes of Normal Form Games

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  • Fabrizio Germano

Abstract

Equivalence classes of normal form games are defined using the discontinuities of correspondences of standard equilibrium concepts like correlated, Nash, and robust equilibrium, or risk dominance and rationalizability. Resulting equivalence classes are fully characterized and compared across different equilibrium concepts for 2 x 2 games; larger games are also considered. It is argued that the procedure leads to broad and game-theoretically meaningful distinctions of games as well as to alternative ways of representing, comparing and testing equilibrium concepts.

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  • Fabrizio Germano, 2003. "On Some Geometry and Equivalence Classes of Normal Form Games," Working Papers 42, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:42
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    Cited by:

    1. Joseph Abdou & Nikolaos Pnevmatikos & Marco Scarsini, 2014. "Uniformity and games decomposition," Documents de travail du Centre d'Economie de la Sorbonne 14084r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Mar 2017.
    2. John Duffy & Dietmar Fehr, 2018. "Equilibrium selection in similar repeated games: experimental evidence on the role of precedents," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 573-600, September.
    3. Luke Marris & Ian Gemp & Georgios Piliouras, 2023. "Equilibrium-Invariant Embedding, Metric Space, and Fundamental Set of $2\times2$ Normal-Form Games," Papers 2304.09978, arXiv.org.
    4. Inarra, E. & Larrea, C. & Saracho, A., 2014. "The von Neumann–Morgenstern stable sets for the mixed extension of 2×2 games," Economics Letters, Elsevier, vol. 125(1), pages 70-73.
    5. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.
    6. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.

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    More about this item

    Keywords

    Non-cooperative games; classification and equivalence classes; experimental games; geometry of games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

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