Robust game theory |
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Authors: | Michele Aghassi Dimitris Bertsimas |
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Institution: | (1) Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;(2) Boeing Professor of Operations Research, Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, E53-363, Cambridge, MA 02139, USA |
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Abstract: | 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.
The research of the author was partially supported by a National Science Foundation Graduate Research Fellowship and by the
Singapore-MIT Alliance.
The research of the author was partially supported by the Singapore-MIT Alliance. |
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Keywords: | Game theory Robust optimization Bayesian games Ex post equilibria |
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