Optimal Private Payoff Manipulation against Commitment in Extensive-form Games
This addresses a strategic deception problem in game theory for followers seeking to exploit leaders' learning mechanisms, representing an incremental advance in manipulation analysis.
The paper tackles the problem of a follower optimally manipulating a leader's strategy commitment in extensive-form games by misreporting private payoff information, showing that it is polynomial-time tractable to find the optimal misreporting strategy and characterizing all inducible game outcomes.
To take advantage of strategy commitment, a useful tactic of playing games, a leader must learn enough information about the follower's payoff function. However, this leaves the follower a chance to provide fake information and influence the final game outcome. Through a carefully contrived payoff function misreported to the learning leader, the follower may induce an outcome that benefits him more, compared to the ones when he truthfully behaves. We study the follower's optimal manipulation via such strategic behaviors in extensive-form games. Followers' different attitudes are taken into account. An optimistic follower maximizes his true utility among all game outcomes that can be induced by some payoff function. A pessimistic follower only considers misreporting payoff functions that induce a unique game outcome. For all the settings considered in this paper, we characterize all the possible game outcomes that can be induced successfully. We show that it is polynomial-time tractable for the follower to find the optimal way of misreporting his private payoff information. Our work completely resolves this follower's optimal manipulation problem on an extensive-form game tree.