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Simple Sufficient Conditions for Weak Reciprocal Upper Semi-Continuity in Extended Games

Author

Listed:
  • Blake Allison

    (Department of Economics, Emory University)

  • Adib Bagh

    (Department of Economics and Mathematics, University of Kentucky)

  • Jason Lepore

    (Department of Economics, California Polytechnic State University)

Abstract

We provide a sufficient condition for a game with discontinuous payoffs to be weakly reciprocally upper semi-continuous in mixed strategies. This condition is imposed on the individual payoffs and not on their sum, and it can be readily verified in a large class of games even when the sum of payoffs in such games is not upper semi-continuous. We apply our result to establish the existence of mixed strategy equilibria in probabilistic voting competitions when candidates have heterogenous beliefs about the distribution of the voters.

Suggested Citation

  • Blake Allison & Adib Bagh & Jason Lepore, 2016. "Simple Sufficient Conditions for Weak Reciprocal Upper Semi-Continuity in Extended Games," Working Papers 1608, California Polytechnic State University, Department of Economics.
    • Handle: RePEc:cpl:wpaper:1608
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    File URL: https://www.cob.calpoly.edu/economics/wp-content/uploads/sites/27/2019/11/paper1608.pdf
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    More about this item

    Keywords

    Better reply security; extended games; Weak reciprocal upper semi-continuity; Nash equilibria; Probabilistic voting models.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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