Nash equilibrium in games with quasi-monotonic best-responses

Rabah Amir () and Luciano De Castro

Journal of Economic Theory, 2017, vol. 172, issue C, 220-246

Abstract: This paper proposes a new general class of strategic games and develops an associated new existence result for pure-strategy Nash equilibrium. For a two-player game with scalar and compact action sets, existence entails that one reaction curve be increasing and continuous and the other quasi-increasing (i.e., not have any downward jumps). The latter property amounts to strategic quasi-complementarities. The paper provides a number of ancillary results of independent interest, including sufficient conditions for a quasi-increasing argmax (or non-monotone comparative statics), and new sufficient conditions for uniqueness of fixed points. For maximal accessibility of the results, the main results are presented in a Euclidean setting. We argue that all these results have broad and elementary applicability by providing simple illustrations with commonly used models in economic dynamics and industrial organization.

Keywords: Existence of Nash equilibrium; Uniqueness of Nash equilibrium; Quasi-monotone functions; Non-monotone comparative statics; Supermodularity; Tarski's Theorem (search for similar items in EconPapers)
JEL-codes: C72 D43 L13 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:172:y:2017:i:c:p:220-246

DOI: 10.1016/j.jet.2017.09.004

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