Agents engaged in noncooperative interaction may seek to achieve a 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 that the agents perceive–the implicit game.

If estimation of rewards is based on modeling, agents may err. We define a robust equilibrium, which is impervious to slight perturbations, and prove that one can be efficiently pinpointed. We then 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.

Assuming that valuations for different outcomes of the game are reported by agents in advance of play, agents may choose to report false rewards in order to improve their eventual payoff. We define the Game-Manipulation (GM) decision problem, and fully characterize the complexity of this problem and some variants.