Robust game theory

We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our "robust game" model relaxes the assumptions of Harsanyi's Bayesian game mode...

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Bibliographic Details
Published in:Mathematical programming 2006-06, Vol.107 (1-2), p.231-273
Main Authors: Aghassi, Michele, Bertsimas, Dimitris
Format: Article
Language:English
Subjects:
Economic models
Equilibrium
Equilibrium methods
Game theory
Games
Knowledge
Nobel prizes
Operations research
Optimization
Probability distribution
Robustness
Scholarships & fellowships
Studies
Uncertainty
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Summary:We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our "robust game" model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call "robust-optimization equilibrium," to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results. [PUBLICATION ABSTRACT]
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-005-0686-0