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On the solution of games with arbitrary payoffs: An application to an over-the-counter financial market

Author

Listed:
  • Iraklis Kollias
  • John Leventides
  • Vassilios G. Papavassiliou

    (National and Kapodistrian University of Athens, University College Dublin, and UCD Geary Institute for Public Policy, University College Dublin)

Abstract

This paper defines a variety of game theoretic solution concepts in the language of soft set theory. We begin by defining the Nash equilibrium in pure strategies. We assume that the gains of the players are totally ordered and non-desirable alternatives are absent. Moreover, we introduce the notions of strong and semi-strong utility. These two completely new notions, serve as a mechanism for converting non-ordered gains into totally ordered ones. We define the Nash equilibrium in mixed strategies in a general framework by introducing the notion of an extended game and strategy space. We finally define the Nash solution to cooperative bargaining games within the framework of soft set theory, illustrate a practical application to an over-the-counter (OTC) financial market, and provide a detailed numerical example

Suggested Citation

  • Iraklis Kollias & John Leventides & Vassilios G. Papavassiliou, 2022. "On the solution of games with arbitrary payoffs: An application to an over-the-counter financial market," Working Papers 202302, Geary Institute, University College Dublin.
    • Handle: RePEc:ucd:wpaper:202302
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    More about this item

    Keywords

    Game theory; Soft set theory; Nash equilibrium; Cooperative bargaining games; Over-the-counter financial markets; Financial intermediation;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • G1 - Financial Economics - - General Financial Markets

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