Robust optimization with applications to game theory

Abstract

In this article, we investigate robust optimization equilibria with two players, in which each player can neither evaluate his opponent's strategy nor his own cost matrix accurately while may estimate a bounded set of the strategy or cost matrix. We obtain a result that solving this equilibria can be formulated as solving a second-order cone complementarity problem under an ellipsoid uncertainty set or a mixed complementarity problem under a box uncertainty set. We present some numerical results to illustrate the behaviour of robust optimization equilibria.

Keywords:

• robust optimization equilibria
• bimatrix game
• strategy uncertainty
• cost matrix uncertainty
• second-order cone complementarity problem
• mixed complementarity problem

AMS Subject Classifications::

• 74P05
• 65K10

Acknowledgement

This work was supported by the NSF of China under grant No. 10771057.