Mathematical Programming

, Volume 107, Issue 1–2, pp 231–273 | Cite as

Robust game theory

  • Michele Aghassi
  • Dimitris BertsimasEmail author


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.


Game theory Robust optimization Bayesian games Ex post equilibria 

Mathematics Subject Classification (2000)

90C05 90C47 91A06 91A10 91A15 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Operations Research CenterMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Boeing Professor of Operations Research, Sloan School of Management and Operations Research CenterMassachusetts Institute of TechnologyCambridgeUSA

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