  We study the role of costly information in non-cooperative two-player games
when an extrinsic third party information broker is introduced asymmetrically,
allowing one player to obtain information about the other player's action. This
broker or "oracle" is defined by a probability of response, supplying correct
information randomly; the informed player can pay more for a higher probability
of response. We determine the necessary and sufficient conditions for strategy
profiles to be equilibria, in terms of how both players change their strategies
in response to the existence of the oracle, as determined by its cost of
information function. For mixed strategy equilibria, there is a continuous
change as information becomes cheaper, with clear transitions occuring at
critical {\it nodes} at which pure strategies become dominated (or
undominated). These nodes separate distinct responses to the information for
sale, alternating between regions where the paying player increases the amount
of information purchased, and regions where the other player moves away from
riskier strategies, in favor of safer bets that minimize losses. We derive
conditions for these responses by defining a value of information.
