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

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  • Iraklis Kollias
  • John Leventides
  • Vassilios G. Papavassiliou

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 financial market, and provide a detailed numerical example.

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  • Iraklis Kollias & John Leventides & Vassilios G. Papavassiliou, 2024. "On the solution of games with arbitrary payoffs: An application to an over‐the‐counter financial market," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 1877-1895, April.
    • Handle: RePEc:wly:ijfiec:v:29:y:2024:i:2:p:1877-1895
    DOI: 10.1002/ijfe.2758
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    More about this item

    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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