Unilateral incentive alignment in two-agent stochastic games

Multiagent learning is challenging when agents face mixed-motivation interactions, where conflicts of interest arise as agents independently try to optimize their respective outcomes. Recent advancements in evolutionary game theory have identified a class of "zero-determinant" strategies, which confer an agent with significant unilateral control over outcomes in repeated games. Building on these insights, we present a comprehensive generalization of zero-determinant strategies to stochastic games, encompassing dynamic environments. We propose an algorithm that allows an agent to discover strategies enforcing predetermined linear (or approximately linear) payoff relationships. Of particular interest is the relationship in which both payoffs are equal, which serves as a proxy for fairness in symmetric games. We demonstrate that an agent can discover strategies enforcing such relationships through experience alone, without coordinating with an opponent. In finding and using such a strategy, an agent ("enforcer") can incentivize optimal and equitable outcomes, circumventing potential exploitation. In particular, from the opponent's viewpoint, the enforcer transforms a mixed-motivation problem into a cooperative problem, paving the way for more collaboration and fairness in multiagent systems.