A Difficulty in Characterising Mixed Nash Equilibria in a Strategic Market Game

Ralph W. Bailey (), Maria Kozlovskaya () and Indrajit Ray ()
Additional contact information
Ralph W. Bailey: Department of Economics, University of Birmingham, UK
Maria Kozlovskaya: Economics, Finance and Entrepreneurship Department, Aston Business School, Aston University, UK

No E2025/21, Cardiff Economics Working Papers from Cardiff University, Cardiff Business School, Economics Section

Abstract: We study mixed-strategy equilibria in a two-good buy-and-sell strategic market game à la Shapley–Shubik. We show that expected utility need not be quasiconcave in strategies, creating difficulties for characterising mixed equilibria. We prove that any mixed Nash profile in which each player mixes over only two positive bids is purifiable and the implied outcome is a mixture over pure equilibria.

Keywords: Mixed bids; Mixed strategy Nash equilibrium; Strategic market games (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2025-10
New Economics Papers: this item is included in nep-com, nep-gth, nep-mic and nep-upt
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Working Paper: A Difficulty in Characterising Mixed Nash Equilibria in a Strategic Market Game (2023)
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