  In some games, additional information hurts a player, e.g., in games with
first-mover advantage, the second-mover is hurt by seeing the first-mover's
move. What properties of a game determine whether it has such negative "value
of information" for a particular 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 define the marginal utility of a
parameter vector specifying a game. So rather than analyze the global structure
of the relationship between a game's parameter vector and player behavior, as
in previous work, we focus on the local structure of that relationship. This
allows us to prove that generically, every game can have negative marginal
value of information, unless one imposes a priori constraints on allowed
changes to the game's parameter vector. We demonstrate these and related
results numerically, and discuss their implications.
