Existence and Uniqueness of Nash Equilibrium in Aggregative Games: An Expository Treatment

Richard Cornes and Takashi Sato ()
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Takashi Sato: Shimonoseki City University

A chapter in Equilibrium Theory for Cournot Oligopolies and Related Games, 2016, pp 47-61 from Springer

Abstract: Abstract In this study, we present an elementary treatment of Cournot’s oligopolistic competition model in which an industry’s demand function has a constant elasticity and technology has a convex cost function. Our treatment uses the ‘share function’, which exploits the aggregative structure of the resulting game. In this setting, the best response functions are not monotonic, ruling out the use of techniques previously applied to analyze submodular and supermodular games. Share functions, which model each firm’s most preferred share of total output as a proportion of total output, allow for a direct and transparent method to derive the properties of a Nash equilibrium. To illustrate this, we establish the existence of a unique equilibrium and examine its response to exogenous shocks.

Keywords: Nash Equilibrium; Demand Function; Replacement Function; Share Function; Consistency Requirement (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spschp:978-3-319-29254-0_5

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DOI: 10.1007/978-3-319-29254-0_5

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