Robust games: theory and application to a Cournot duopoly model

Giovanni Paolo Crespi (), Davide Radi () and Matteo Rocca ()
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Giovanni Paolo Crespi: Università degli studi dell’Insubria
Matteo Rocca: Università degli studi dell’Insubria

Decisions in Economics and Finance, 2017, vol. 40, issue 1, No 10, 177-198

Abstract: Abstract In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value $$\epsilon $$ ϵ such that robust-optimization equilibria are a subset of $$\epsilon $$ ϵ -Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for $$\epsilon $$ ϵ -Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.

Keywords: Robust games; Robust-optimization equilibrium; Robust Cournot duopoly game; Robust optimization (search for similar items in EconPapers)
JEL-codes: C61 C72 D21 D43 D81 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10203-017-0199-3

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