Payoff Control in Multichannel Games: Influencing Opponent Learning Evolution

In this article, we introduce a new theory for payoff control in multichannel learning environments, where agents interact with each other over multiple channels and each channel is a repeated normal form game. We propose two payoff control strategies - partial control and full control - that allow a single agent to set an upper bound to the opponent's expected payoffs summed across all channels, even if the opponent is a reinforcement learning agent. We prove that a partial (or full) control strategy can be obtained by solving a system of inequalities, and characterize the conditions under which such a partial (or full) control strategy exists. We show that by utilizing these control strategies, the agent can influence the opponent's learning evolution and direct it toward a desired viable equilibrium. Our experiments confirm the effectiveness of our theory for payoff control in a wide range of multichannel learning environments.