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.
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Co-author: Rabah Amir
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.
JEL classification:
C72; D43; L13
Keywords:
Existence of Nash equilibrium; Uniqueness of Nash equilibrium; Quasi-monotone functions; Non-monotone comparative statics; Supermodularity; Tarski’s Theorem
Citation:
Amir, R. and de Castro, L. (2017), “Nash Equilibrium in Games with Quasi-Monotonic Best-Responses”, Journal of Economic Theory, 172, 220-246.