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

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

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


Authors

R. A. Edwards

R. R. Routledge



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 Science and Business Media LLC
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

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