Nash equilibrium in games with quasi-monotonic best-responses

• 成果类型: Article
• 署名作者: Amir, Rabah; De Castro, Luciano
• 署名单位: University of Iowa
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2017.09.004
• 发表日期: 2017
• 页码: 220-246
• 关键词: Existence of Nash equilibrium; Uniqueness of Nash equilibrium; Quasi-monotone functions; Non-monotone comparative statics; supermodularity; Tarski's Theorem

摘要

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. (C) 2017 Elsevier Inc. All rights reserved.