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Operations Research Transactions >

2024 , Vol. 28 >Issue 3: 132 - 142

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.03.009

Interpretations of the nonexistence of equilibrium in game theory and economics

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  • 1. School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China
    2. Beijing Laboratory of National Economic Security Early-warning Engineering, Beijing Jiaotong University, Beijing 100044, China

Received date: 2024-03-29

  Online published: 2024-09-07

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, 2024, All rights reserved, without authorization
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Abstract

The refinement and formalization of equilibrium concepts mark the establishment of game theory as a distinct discipline. The development of game theory has been centered around the fundamental properties of various equilibrium concepts. It is generally accepted that the nonexistence of equilibrium is seen as a negative outcome, impeding the advancement of equilibrium research. This holds true for economic research as well. This paper illustrates, through two examples from the literature on non-cooperative games and perfectly competitive markets, that sometimes valuable interpretations can be provided for the nonexistence of equilibrium. The first example examines the evolution of fashion phenomena through a network game based on matching pennies, where the nonexistence of equilibrium is used to interpret the emergence of fashion cycles. The second example discusses the matching problem between companies and workers in a perfectly competitive labor market, where the nonexistence of equilibrium is used to explain the phenomenon of early contracting. Additionally, we briefly introduce Shapley's insightful interpretation regarding the empty core in transferable utility cooperative games.

Key words： game theory; Nash equilibrium; core; competitive equilibrium

Cite this article

Zhigang CAO, Jin SONG, Sijie WANG, Feng ZHU . Interpretations of the nonexistence of equilibrium in game theory and economics[J]. Operations Research Transactions, 2024 , 28(3) : 132 -142 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.03.009

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