Pride and Perjury: A Computational Characterization of Multiagent Games with Fallacious Rewards

Agents engaged in noncooperative interplay often seek convergence to Nash equilibrium; this requires that agents be aware of others’ rewards. Misinformation about rewards leads to a gap between the real interaction model — the explicit game — and the game which the agents perceive — the implicit game. We identify two possible sources of fallacious rewards: pride and perjury. If estimation of rewards is based on modeling, a proud agent is likely to err. We define a robust equilibrium, which is impervious to slight perturbations, and prove that one can be efficiently pinpointed. We relax this concept by introducing persistent equilibrium pairs — pairs of equilibria of the explicit and implicit games with nearly identical rewards — and resolve associated complexity questions. Supposing agents simply reveal their valuations for different outcomes of the game, perjuring agents may report false rewards in order to improve their payoff. We define the Game-Manipulation (GM) decision problem, and fully characterize the complexity of this problem and some variations.