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

Edwards, R. A.; Routledge, R. R.

Abstract

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.

Citation

Edwards, R. A., & Routledge, R. R. (2023). Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization. International Journal of Game Theory, 52, 569-586. https://doi.org/10.1007/s00182-022-00830-3

• Journal Article Type: Article
• Acceptance Date: Oct 30, 2022
• Online Publication Date: Nov 29, 2022
• Publication Date: 2023-06
• Deposit Date: Nov 30, 2022
• Publicly Available Date: Dec 1, 2022
• Journal: International Journal of Game Theory
• Print ISSN: 0020-7276
• Electronic ISSN: 1432-1270
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Pages: 569-586
• DOI: https://doi.org/10.1007/s00182-022-00830-3
• Keywords: General Medicine; General Chemistry
• Public URL: https://nottingham-repository.worktribe.com/output/14314160
• Publisher URL: https://link.springer.com/article/10.1007/s00182-022-00830-3