Computing Optimal Commitments to Strategies and Outcome-Conditional Utility Transfers

Nathaniel Sauerberg, Caspar Oesterheld

Abstract: Prior work has studied the computational complexity of computing optimal strategies to commit to in Stackelberg or leadership games, where a leader commits to a strategy which is observed by one or more followers. We extend this setting to one where the leader can additionally commit to outcome-conditional utility transfers. We characterize the computational complexity of finding optimal strategies in normal-form and Bayesian games, giving a mix of efficient algorithms and NP-hardness results. Finally, we allow the leader to also commit to a signaling scheme which induces a correlated equilibrium. In this setting, optimal commitments can be found in polynomial time for arbitrarily many players.