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Extended Nash Equilibria of Nonmonetized Noncooperative Games on Preordered Sets

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  • Jinlu Li

    (Department of Mathematics, Shawnee State University, Portsmouth, Ohio 45662, USA)

Abstract

A noncooperative game is said to be nonmonetized if the ranges of the utilities (payoffs) of the players are preordered sets. In this paper, we examine some nonmonetized noncooperative games in which both of the collection of strategies and the ranges of the utilities for the players are preordered sets. Then, we spread the concept of extended Nash equilibria of noncooperative games from posets to preordered sets. By applying some fixed point theorems on preordered sets and by using the order preserving property of the utilities, we prove an existence theorem of extended Nash equilibria for nonmonetized noncooperative games.

Suggested Citation

  • Jinlu Li, 2015. "Extended Nash Equilibria of Nonmonetized Noncooperative Games on Preordered Sets," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-13.
    • Handle: RePEc:wsi:igtrxx:v:17:y:2015:i:01:n:s0219198915400095
    DOI: 10.1142/S0219198915400095
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    Cited by:

    1. Kokkala, Juho & Poropudas, Jirka & Virtanen, Kai, 2015. "Rationalizable Strategies in Games With Incomplete Preferences," MPRA Paper 68331, University Library of Munich, Germany.

    More about this item

    Keywords

    Preordered set; order preserving mapping; generalized Nash equilibrium; extended Nash equilibrium; 46B42; 47H10; 58J20; 91A10;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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