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

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

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

Abstract: We analyse the conditions for a strategy profile to be an equilibrium in a specific buy and sell strategic market game, with two goods, using best responses of a player against random bids from the opponents. The difficulty in characterising mixed Nash equilbria is that the expected utility is not quasiconcave in strategies. We still prove that any mixed strategy Nash equilibrium profile in which every player faces only two random bids is trivial, that is, is a convex combination of some pure strategy Nash equilibria; moreover, we show that the outcome (the price and the allocations) is deterministic in such an equilibrium.

Keywords: Mixed bids; Mixed strategy Nash equilibrium; strategic market games JEL codes: C72 (search for similar items in EconPapers)
Date: 2023
New Economics Papers: this item is included in nep-com, nep-gth, nep-mic and nep-upt
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