Article ID: | iaor20133250 |
Volume: | 39 |
Issue: | 2 |
Start Page Number: | 109 |
End Page Number: | 114 |
Publication Date: | Mar 2011 |
Journal: | Operations Research Letters |
Authors: | Jeyakumar V, Li G Y, Lee G M |
Keywords: | minimax problem, uncertainty |
The celebrated von Neumann minimax theorem is a fundamental theorem in two‐person zero‐sum games. In this paper, we present a generalization of the von Neumann minimax theorem, called robust von Neumann minimax theorem, in the face of data uncertainty in the payoff matrix via robust optimization approach. We establish that the robust von Neumann minimax theorem is guaranteed for various classes of bounded uncertainties, including the matrix 1‐norm uncertainty, the rank‐1 uncertainty and the columnwise affine parameter uncertainty.