Rank Reduction in Bimatrix Games

The rank of a bimatrix game is defined as the rank of the sum of the payoff matrices of the two players. Under certain conditions on the payoff matrices, we devise a method that reduces the rank of the game without changing the equilibrium of the game. We leverage matrix pencil theory and Wedderburn rank reduction formula to arrive at our results. We also present a constructive proof of the fact that in a generic square game, the rank of the game can be reduced by 1, and in generic rectangular game, the rank of the game can be reduced by 2 under certain assumptions.
Abhishek Gupta is an assistant professor in the ECE department at The Ohio State University. He completed his PhD in Aerospace Engineering from UIUC in 2014. His research interests are in stochastic control theory, probability theory, and game theory with applications to transportation markets, electricity markets, and cybersecurity of control systems.