Safe Equilibrium

In designing a strategy for a multiagent interaction an agent must balance between the assumption that opponents are behaving rationally with the risks that may occur if opponents behave irrationally. Most classic game-theoretic solution concepts, such as Nash equilibrium (NE), assume that all players are behaving rationally (and that this fact is common knowledge). On the other hand, a maximin strategy plays a strategy that has the largest worst-case guaranteed expected payoff; this limits the potential downside against a worstcase and potentially irrational opponent, but can also cause us to achieve significantly lower payoff against rational opponents. In two-player zero-sum games, Nash equilibrium and maximin strategies are equivalent (by the minimax theorem), and these two goals are completely aligned. But in non-zero-sum games and games with more than two players, this is not the case. In these games we can potentially obtain arbitrarily low payoff by following a Nash equilibrium strategy, but if we follow a maximin strategy will likely be playing far too conservatively. While the assumption that opponents are exhibiting a degree of rationality, as well as the desire to limit worst-case performance in the case of irrational opponents, are both desirable, neither the Nash equilibrium nor maximin solution concept is definitively compelling on its own. We propose a new solution concept that balances between these two extremes.