IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/669.html
   My bibliography  Save this paper

On some geometry and equivalence classes of normal form games

Author

Abstract

Equivalence classes of normal form games are defined using the geometry of correspondences of standard equilibiurm 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. It is argued that the procedure can lead to broad and game-theoretically meaningful distinctions of games as well as to alternative ways of viewing and testing equilibrium concepts. Larger games are also briefly considered.

Suggested Citation

  • Fabrizio Germano, 2003. "On some geometry and equivalence classes of normal form games," Economics Working Papers 669, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:669
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/669.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Atsushi Kajii & Stephen Morris, 1997. "Refinements and Social Order Beliefs: A Unified Survey," Discussion Papers 1197, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 387-430, June.
    5. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
    6. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "Regret-Based Continuous-Time Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 5, pages 99-124, World Scientific Publishing Co. Pte. Ltd..
    8. 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.
    9. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, September.
    10. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
    11. Antonio Cabrales & Rosemarie Nagel & Roc Armenter, 2007. "Equilibrium selection through incomplete information in coordination games: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 221-234, September.
    12. GERMANO, Fabrizio, 1998. "On Nash equivalence classes of generic normal form games," LIDAM Discussion Papers CORE 1998033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Straub, Paul G., 1995. "Risk dominance and coordination failures in static games," The Quarterly Review of Economics and Finance, Elsevier, vol. 35(4), pages 339-363.
    14. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-764, May.
    15. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    16. Van Damme, Eric, 2002. "Strategic equilibrium," 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 41, pages 1521-1596, Elsevier.
    17. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
    18. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    19. McLennan, Andrew, 1997. "The Maximal Generic Number of Pure Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 408-410, February.
    20. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    21. Barany, I & Lee, J & Shubik, M, 1992. "Classification of Two-Person Ordinal Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 267-290.
    22. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, September.
    23. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    24. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    25. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, September.
    26. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antonio Cabrales & Rosemarie Nagel & Roc Armenter, 2007. "Equilibrium selection through incomplete information in coordination games: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 221-234, September.
    2. Rui SILVA, 2018. "Equilibrium Selection in n-Person Static Games with Complete Information," Departmental Working Papers 2018-04, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    4. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
    5. Giovanna Devetag, 2000. "Transfer, Focality and Coordination: Some Experimental Results," LEM Papers Series 2000/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    6. López-Pérez, Raúl & Pintér, Ágnes & Kiss, Hubert J., 2015. "Does payoff equity facilitate coordination? A test of Schelling's conjecture," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 209-222.
    7. Colin Camerer & Teck-Hua Ho & Juin Kuan Chong, 2003. "A cognitive hierarchy theory of one-shot games: Some preliminary results," Levine's Bibliography 506439000000000495, UCLA Department of Economics.
    8. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    9. Zambrano, Eduardo, 2008. "Epistemic conditions for rationalizability," Games and Economic Behavior, Elsevier, vol. 63(1), pages 395-405, May.
    10. John Van Huyck & Dale O. Stahl, 2018. "Conditional behavior and learning in similar stag hunt games," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 513-526, September.
    11. Cubitt, Robin P. & Sugden, Robert, 2014. "Common Reasoning In Games: A Lewisian Analysis Of Common Knowledge Of Rationality," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 285-329, November.
    12. Robin P. Cubitt & Robert Sugden, 2008. "Common reasoning in games," Discussion Papers 2008-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    13. GERMANO, Fabrizio, 1998. "On Nash equivalence classes of generic normal form games," LIDAM Discussion Papers CORE 1998033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
    15. Maruta, Toshimasa & Okada, Akira, 2012. "Stochastically stable equilibria in n-person binary coordination games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 31-42.
    16. Dimitri Dubois & Marc Willinger & Phu Nguyen Van, 2008. "Optimization incentive and relative riskiness in experimental coordination games," Working Papers 08-19, LAMETA, Universtiy of Montpellier, revised Nov 2008.
    17. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    18. D. Dubois & M. Willinger & P. Van Nguyen, 2012. "Optimization incentive and relative riskiness in experimental stag-hunt games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 369-380, May.
    19. Cubitt, Robin P. & Sugden, Robert, 2014. "Common Reasoning In Games: A Lewisian Analysis Of Common Knowledge Of Rationality," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 285-329, November.
    20. Antonio Cabrales & Michalis Drouvelis & Zeynep Gurguy & Indrajit Ray, 2017. "Transparency is Overrated: Communicating in a Coordination Game with Private Information," CESifo Working Paper Series 6781, CESifo.

    More about this item

    Keywords

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

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:669. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.