Strategic Achilles: Is Prior Information About Your Opponent’s Strategy Valuable?∗

Is having prior information about your opponent’s strategy helpful? We investigate this question using an adaptive framework where agents must implement their strategies as finite automata. Some agents are informed of the strategic complexity of their opponents and condition their strategies on that information. Intuitively, one might think that such strategic information should be advantageous, or at least should never hurt since it can be ignored. Notwithstanding this intuition, we find that informed agents do slightly worse than uninformed ones across a wide class of games. In fact, there is a class of games where they do significantly worse. This latter result is tied to the need of the informed agents to condition their strategies on the complexity of their opponents, leaving them vulnerable to manipulation after periods when certain levels of complexity do not arise in the uninformed population. Hence, any benefits accrued to the informed agents by their enhanced abilities come at a potential cost, just as the mythical Achilles could only become immortal by being vulnerable at the heel.