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Strategic Complements in Two Stage, 2 × 2 Games

Author

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  • Yue Feng

    (Department of Economics, The University of Kansas)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

Abstract

Strategic complements are well understood for normal form games, but less so for extensive form games. Indeed, there is some evidence that extensive form games with strategic complemen- tarities are a very restrictive class of games (Echenique (2004)). We explore the extent of this restrictiveness in the context of two stage, 2×2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. In contrast, the set of games that exhibit strategic complements (in the sense of increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2 × 2 games (and provides a basis for possibly greater scope in more general games). Moreover, the set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice.

Suggested Citation

  • Yue Feng & Tarun Sabarwal, 2019. "Strategic Complements in Two Stage, 2 × 2 Games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201906, University of Kansas, Department of Economics.
    • Handle: RePEc:kan:wpaper:201906
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    File URL: http://www2.ku.edu/~kuwpaper/2019Papers/201906.pdf
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    References listed on IDEAS

    as
    1. Walker, Mark & Wooders, John & Amir, Rabah, 2011. "Equilibrium play in matches: Binary Markov games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 487-502, March.
    2. Tarun Sabarwal & Hoa VuXuan, 2018. "Two Stage 2 × 2 Games With Strategic Substitutes and Strategic Heterogeneity," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201902, University of Kansas, Department of Economics.
    3. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    4. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    5. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
    6. Roy, Sunanda & Sabarwal, Tarun, 2010. "Monotone comparative statics for games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 793-806, September.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. Xavier Vives, 2009. "Strategic complementarity in multi-stage games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 151-171, July.
    9. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
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    Cited by:

    1. Tarun Sabarwal & Hoa VuXuan, 2018. "Two Stage 2 × 2 Games With Strategic Substitutes and Strategic Heterogeneity," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201902, University of Kansas, Department of Economics.
    2. Tarun Sabarwal, 2023. "Universal Theory of Equilibrium in Models with Complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202312, University of Kansas, Department of Economics, revised Nov 2023.

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    More about this item

    Keywords

    Strategic complements; extensive form game; two stage game;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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