Games with espionage

We consider normal form games in which two players decide on their strategies before the start of play and Player 1 can purchase noisy information about his opponent's decisions concerning future response policies (i.e., spy on his opponent). We give a full characterization of the set of distributions over the players' payoffs that can be induced by such equilibria, as well as describe their welfare and Pareto properties. In 2 × 2 games we find three equilibrium phenomena: (i) when the game is non-degenerate, the information purchased is independent of its cost. The cost determines only whether information is purchased or not, (ii) the player who spies treats his information as if it were deterministic, even though it is correct only probabilistically, and (iii) in chain store models, espionage is used if and only if the perfect equilibrium payoff differs from the Stackelberg equilibrium payoff with Player 2 being the Stackelberg leader.