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A non-robustness in the order structure of the equilibrium set in lattice games

Author

Listed:
  • Andrew Monaco

    (Department of Economics, University of Kansas)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

Abstract

The order and lattice structure of the equilibrium set in games with strategic complements do not survive a minimal introduction of strategic substitutes: in a lattice game in which all-but-one players exhibit strategic complements (with one player exhibiting strict strategic complements), and the remaining player exhibits strict strategic substitutes, no two equilibria are comparable. More generally, in a lattice game, if either (1) just one player has strict strategic complements and another player has strict strategic substitutes, or (2) just one player has strict strategic substitutes and has singleton-valued best-responses, then without any restrictions on the strategic interaction among the other players, no two equilibria are comparable. In such cases, the equilibrium set is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Moreover, in such cases, with linearly ordered strategy spaces, the game has at most one symmetric equilibrium. Several examples are presented.

Suggested Citation

  • Andrew Monaco & Tarun Sabarwal, 2010. "A non-robustness in the order structure of the equilibrium set in lattice games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201004, University of Kansas, Department of Economics, revised Aug 2011.
    • Handle: RePEc:kan:wpaper:201004
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    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201004.pdf
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    References listed on IDEAS

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    1. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
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    Cited by:

    1. Magnus Hoffmann & Grégoire Rota‐Graziosi, 2020. "Endogenous timing in the presence of non‐monotonicities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 359-402, February.
    2. Andrew Monaco & Tarun Sabarwal, 2012. "Monotone Comparative Statics in Games with both Strategic Complements and Strategic Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201236, University of Kansas, Department of Economics, revised Aug 2012.

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    More about this item

    Keywords

    Lattice games; strategic complements; strategic substitutes; equilibrium set;
    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

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