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Learning in games with strategic complementarities revisited

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  • Berger, Ulrich

Abstract

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.

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  • Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    • Handle: RePEc:eee:jetheo:v:143:y:2008:i:1:p:292-301
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    2. Karl H. Schlag & Péter Vida, 2014. "Believing when Credible: Talking about Future Plans," Vienna Economics Papers 1409, University of Vienna, Department of Economics.
    3. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    4. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2023. "The logit dynamic in supermodular games with a continuum of strategies: A deterministic approximation approach," Games and Economic Behavior, Elsevier, vol. 139(C), pages 133-160.
    5. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
    6. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. van Strien, Sebastian & Sparrow, Colin, 2011. "Fictitious play in 3x3 games: Chaos and dithering behaviour," Games and Economic Behavior, Elsevier, vol. 73(1), pages 262-286, September.
    8. Schlag, Karl H. & Vida, Péter, 2015. "Believing when Credible: Talking about Future Plans and Past Actions," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 517, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    9. Schlag, Karl H. & Vida, Péter, 2013. "Commitments, Intentions, Truth and Nash Equilibria," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 438, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    10. Karl H. Schlag & Péter Vida, 2014. "Believing when Credible: Talking about Future Plans," Vienna Economics Papers vie1409, University of Vienna, Department of Economics.
    11. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.
    12. Alan Beggs, 2015. "Learning in Monotone Bayesian Games," Economics Series Working Papers 737, University of Oxford, Department of Economics.

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