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Two individuals are involved in a conflict situation in which preferences are ex ante uncertain. Although they eventually learn their own preferences, they have to pay a small cost if they want to secretly learn their opponent's preferences. We show that there is an interval with an upper bound less than 1 and lower bound greater than zero such that, for sufficiently small positive costs of information acquisition, in any Bayesian Nash equilibrium of the resulting game of incomplete information the probability of acquiring information about the opponent's preferences is within this interval.