Distributed Convergence to Nash Equilibria in a Zero-Sum Resource Allocation Game

This paper studies the problem of how to allocate multiple defensive resources to protect multiple sites from possible attacks, which is formulated by a zero-sum resource allocation game with inequality constraints. The considered two classes of players (defenders and attackers) have opposite objectives for a common linear objective function. We put forward a distributed continuous-time algorithm for such problems, and provide a rigorous proof of convergence to a Nash equilibrium. In the end, the efficacy and correctness of our method are illustrated via a numerical example.