A Genetic Algorithm Approach to Compute Mixed Strategy Solutions for General Stackelberg Games

Stackelberg games have found a role in a number of applications including modeling market competition, identifying traffic equilibrium, developing practical security applications and many others. While a number of solution approaches have been developed for these games in a variety of contexts that use mathematical optimization, analytical analysis or heuristic based solutions, literature has been quite sparse on the usage of Genetic Algorithm (GA) based techniques. In this paper, we develop a GA based solution to compute high quality mixed strategy solution for the leader to commit to in a General Stackelberg Game (GSG) using a normal form game formulation. The leader faces multiple types of followers with discrete utility functions where the mixed strategy of the leader (but not the actual action taken in the round) is known to the follower. Our experiments showcase that the GA developed here performs well in terms of scalability and provides reasonably good solution quality in terms of the average reward obtained. Given that finding the optimal mixed strategy solution for GSGs is NP-hard (and the optimal solution for leader lies in the mixed strategy space), we believe that the solution approach presented here can support further development of practical applications using GSGs.