Optimal Machine Strategies to Commit to in Two-Person Repeated Games

The problem of computing optimal strategy to commit to in various games has attracted intense research interests and has important real-world applications such as security (attacker-defender) games. In this paper, we consider the problem of computing optimal leader's machine to commit to in two-person repeated game, where the follower also plays a machine strategy. Machine strategy is the generalized notion of automaton strategy, where the number of states in the automaton can be possibly infinite. We begin with the simple case where both players are confined to automata strategies, and then extend to general (possibly randomized) machine strategies. We first give a concise linear program to compute the optimal leader's strategy and give two efficient implementations of the linear program: one via enumeration of a convex hull and the other via randomization. We then investigate the case where two machines have different levels of intelligence in the sense that one machine is able to record more history information than the other. We show that an intellectually superior leader, sometimes considered being exploited by the follower, can figure out the follower's machine by brute-force and exploit the follower in return.