Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization

Edwards, RA and Routledge, RR ORCID: 0000-0002-0354-4009 (2023) Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization. INTERNATIONAL JOURNAL OF GAME THEORY, 52 (2). pp. 569-586.

Access the full-text of this item by clicking on the Open Access link.

Official URL: http://dx.doi.org/10.1007/s00182-022-00830-3

Abstract

<jats:title>Abstract</jats:title><jats:p>Since (Reny in Econometrica 67:1029–1056, 1999) a substantial body of research has considered what conditions are sufficient for the existence of a pure strategy Nash equilibrium in games with discontinuous payoffs. This work analyzes a general Bertrand game, with convex costs and an arbitrary sharing rule at price ties, in which tied payoffs may be greater than non-tied payoffs when both are positive. On this domain, necessary and sufficient conditions for (i) the existence of equilibrium (ii) the uniqueness of equilibrium are presented. The conditions are intuitively easy to understand and centre around the relationships between intervals of real numbers determined by the primitives of the model.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	Discontinuous payoffs, Existence, Uniqueness, Bertrand competition, Necessary and sufficient conditions
Depositing User:	Symplectic Admin
Date Deposited:	07 Dec 2022 10:14
Last Modified:	27 Nov 2023 06:15
DOI:	10.1007/s00182-022-00830-3
Open Access URL:	https://doi.org/10.1007/s00182-022-00830-3
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3166537