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On ordered equilibria in games with increasing best responses

Author

Listed:
  • Anne-Christine Barthel

    (West Texas A&M University)

  • Eric Hoffmann

    (West Texas A&M University)

Abstract

This paper investigates conditions under which games have totally ordered equilibria, which has implications for the stability as well as the Pareto-ranking of equilibria. We first show that when best responses are strongly increasing, all games with up to three players as well as games with symmetric best responses have totally ordered equilibria. Furthermore, the same results hold when best responses are non-decreasing and equilibria are strict. Non-decreasingness and strong increasingness of best responses are implied by payoffs satisfying the single-crossing and strict single-crossing properties, and hence the former assumptions are weaker than what is assumed in games of strategic complements. Nevertheless, we show that even when the stronger assumption of increasing differences is satisfied, non-symmetric games with more than three players generally do not have totally ordered equilibria.

Suggested Citation

  • Anne-Christine Barthel & Eric Hoffmann, 2024. "On ordered equilibria in games with increasing best responses," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 191-198, December.
    • Handle: RePEc:spr:etbull:v:12:y:2024:i:2:d:10.1007_s40505-024-00272-y
    DOI: 10.1007/s40505-024-00272-y
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    References listed on IDEAS

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    1. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
    2. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    3. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    6. Federico Echenique, 2003. "The equilibrium set of two-player games with complementarities is a sublattice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 903-905, November.
    7. Barthel, Anne-Christine & Hoffmann, Eric, 2023. "On the existence of stable equilibria in monotone games," Journal of Mathematical Economics, Elsevier, vol. 105(C).
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    More about this item

    Keywords

    Strategic complements; Monotone games; Ordered equilibria; Equilibrium chain;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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