A difficulty in characterising mixed Nash equilibria in a strategic market game

Bailey, Ralph W., Kozlovskaya, Maria and Ray, Indrajit ORCID: https://orcid.org/0000-0001-5254-3144 2025. A difficulty in characterising mixed Nash equilibria in a strategic market game. [Discussion Paper]. Cardiff Business School Cardiff Economics Working Papers.

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Abstract

We analyse the conditions for a particular type of mixed strategy profile to be an equilibrium in a specific buy and sell strategic market game `a la Shapley and Shubik (1977), with two goods, using best responses of a player against random bids by the other players. We first identify a difficulty in characterising mixed Nash equilibria; we show that the expected utility is not quasiconcave in strategies. We still prove that any mixed strategy Nash equilibrium profile in which every player faces a mix over only two positive bids is purifiable, that is, is a mixture of some pure strategy Nash equilibrium profiles. Moreover, we prove that the outcome (the price and the allocations) is deterministic in any such equilibrium.

Item Type:	Monograph (Discussion Paper)
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Business (Including Economics)
Subjects:	H Social Sciences > HB Economic Theory
Publisher:	Cardiff Business School Cardiff Economics Working Papers
Date of First Compliant Deposit:	28 October 2025
Last Modified:	28 Oct 2025 11:18
URI:	https://orca.cardiff.ac.uk/id/eprint/181939

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