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Hidden Symmetries and Focal Points

Author

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  • Carlos Al�s-Ferrer
  • Christoph Kuzmics

Abstract

This paper provides a general formal framework to define and analyze the concepts of focal points and frames for normal form games. The information provided by a frame is captured by a symmetry structure which is consistent with the payoff structure of the game. The set of alternative symmetry structures has itself a clear structure (a lattice). Focal points are strategy profiles which respect the symmetry structure and are chosen according to some meta-norm, which is not particular to the framed game at hand. We also clarify the difference between different concepts of symmetry used in the literature.

Suggested Citation

  • Carlos Al�s-Ferrer & Christoph Kuzmics, 2008. "Hidden Symmetries and Focal Points," TWI Research Paper Series 35, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
  • Handle: RePEc:twi:respas:0035
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    References listed on IDEAS

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    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, January.
    2. Blume, Andreas, 2000. "Coordination and Learning with a Partial Language," Journal of Economic Theory, Elsevier, vol. 95(1), pages 1-36, November.
    3. Casajus, Andre, 2000. "Focal Points in Framed Strategic Forms," Games and Economic Behavior, Elsevier, vol. 32(2), pages 263-291, August.
    4. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-595, May.
    5. Mehta, Judith & Starmer, Chris & Sugden, Robert, 1994. "The Nature of Salience: An Experimental Investigation of Pure Coordination Games," American Economic Review, American Economic Association, vol. 84(3), pages 658-673, June.
    6. S. Illeris & G. Akehurst, 2002. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 22(1), pages 1-3, January.
    7. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
    8. Sugden, Robert, 1995. "A Theory of Focal Points," Economic Journal, Royal Economic Society, vol. 105(430), pages 533-550, May.
    9. Binmore, Ken & Samuelson, Larry, 2006. "The evolution of focal points," Games and Economic Behavior, Elsevier, vol. 55(1), pages 21-42, April.
    10. Blume, Andreas & Gneezy, Uri, 2010. "Cognitive forward induction and coordination without common knowledge: An experimental study," Games and Economic Behavior, Elsevier, vol. 68(2), pages 488-511, March.
    11. Maarten Janssen, 2001. "Rationalizing Focal Points," Theory and Decision, Springer, vol. 50(2), pages 119-148, March.
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    Citations

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    Cited by:

    1. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
    2. Wagner, Alexander K. & Granic, Dura-Georg, 2017. "Tie-Breaking Power in Committees," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168187, Verein für Socialpolitik / German Economic Association.
    3. Dietmar Fehr & Frank Heinemann & Aniol Llorente-Saguer, 2011. "The Power of Sunspots: An Experimental Analysis," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_33, Max Planck Institute for Research on Collective Goods.
    4. Fahrenberger, Theresa & Gersbach, Hans, 2010. "Minority voting and long-term decisions," Games and Economic Behavior, Elsevier, vol. 69(2), pages 329-345, July.
    5. Camille Cornand & Frank Heinemann, 2014. "Measuring agents’ reaction to private and public information in games with strategic complementarities," Experimental Economics, Springer;Economic Science Association, vol. 17(1), pages 61-77, March.
    6. Bosch-Domènech, Antoni & Vriend, Nicolaas J., 2013. "On the role of non-equilibrium focal points as coordination devices," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 52-67.
    7. Andonie, Costel & Kuzmics, Christoph & Rogers, Brian W., 2016. "Efficiency based measures of inequality," Center for Mathematical Economics Working Papers 512, Center for Mathematical Economics, Bielefeld University.
    8. Choi, Syngjoo & Gale, Douglas & Kariv, Shachar & Palfrey, Thomas, 2011. "Network architecture, salience and coordination," Games and Economic Behavior, Elsevier, vol. 73(1), pages 76-90, September.
    9. Feicht, Robert & Grimm, Veronika & Rau, Holger A. & Stephan, Gesine, 2015. "On the Impact of Quotas and Decision Rules in Ultimatum Collective Bargaining," IZA Discussion Papers 9506, Institute for the Study of Labor (IZA).
    10. Philipp Külpmann & Davit Khantadze, 2016. "Identifying the Reasons for Coordination Failure in a Laboratory Experiment," 2016 Papers pkl168, Job Market Papers.
    11. Christoph Kuzmics & Daniel Rodenburger, 2018. "A case of evolutionary stable attainable equilibrium in the lab," Graz Economics Papers 2018-05, University of Graz, Department of Economics.
    12. repec:eee:eecrev:v:100:y:2017:i:c:p:175-192 is not listed on IDEAS
    13. Kuzmics, Christoph & Palfrey, Thomas & Rogers, Brian W., 2014. "Symmetric play in repeated allocation games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 25-67.
    14. Ennio Bilancini & Leonardo Boncinelli & Luigi Luini, 2017. "Does Focality Depend on the Mode of Cognition? Experimental Evidence on Pure Coordination Games," Department of Economics University of Siena 771, Department of Economics, University of Siena.

    More about this item

    Keywords

    symmetry; focal points; Nash equilibria;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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