Information Geometry of Noncooperative Games

In some games, additional information hurts a player, e.g., in games with first-mover advan- tage, the second-mover is hurt by seeing the first-mover’s move. What are the conditions for a game to have such negative “value of information” for a player? Can a game have negative value of information for all players? To answer such questions, we generalize the definition of marginal utility of a good (to a player in a decision scenario) to define the marginal utility of a parameter vector specifying a game (to a player in that game). Doing this requires a cardinal information measure; for illustration we use Shannon measures. The resultant formalism reveals a unique ge- ometry underlying every game. It also allows us to prove that generically, every game has negative value of information, unless one imposes a priori constraints on the game’s parameter vector. We demonstrate these and related results numerically, and discuss their implications.