Automated Planning in Repeated Adversarial Games

Game theory’s prescriptive power typically re- lies on full rationality and/or self–play interac- tions. In contrast, this work sets aside these fun- damental premises and focuses instead on hetero- geneous autonomous interactions between two or more agents. Specifically, we introduce a new and concise representation for repeated adversar- ial (constant–sum) games that highlight the nec- essary features that enable an automated plan- ing agent to reason about how to score above the game’s Nash equilibrium, when facing het- erogeneous adversaries. To this end, we present TeamUP, a model–based RL algorithm designed for learning and planning such an abstraction. In essence, it is somewhat similar to R-max with a cleverly engineered reward shaping that treats exploration as an adversarial optimization prob- lem. In practice, it attempts to find an ally with which to tacitly collude (in more than two–player games) and then collaborates on a joint plan of actions that can consistently score a high utility in adversarial repeated games. We use the inaugural Lemonade Stand Game Tournament1 to demonstrate the effectiveness of our approach, and find that TeamUP is the best performing agent, demoting the Tournament’s actual winning strategy into second place. In our experimental analysis, we show hat our strat- egy successfully and consistently builds collabo- rations with many different heterogeneous (and sometimes very sophisticated) adversaries.