Optimal Private Payoff Manipulation against Commitment in Extensive-form Games

TL;DR

This paper analyzes how followers can strategically manipulate their payoff information in extensive-form games to influence outcomes, providing a complete characterization and polynomial-time solutions for optimal misreporting.

Contribution

It introduces a comprehensive framework for understanding and computing the optimal payoff misreporting strategies of followers in extensive-form games, considering different follower attitudes.

Findings

Characterizes all inducible game outcomes through payoff misreporting.

Provides polynomial-time algorithms for followers to find optimal misreports.

Resolves the follower's optimal manipulation problem in extensive-form game trees.

Abstract

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.