Common Knowledge, Ambiguity, and the Value of Information in Games

This paper asks whether the salient result about nonnegative value of cost-free information holds in the context of games. By reexamining Osborne's example where information may hurt, it argues that the failure of this result is mainly driven by the assumption of common knowledge in the traditional framework of incomplete information games, since it leads to act-state dependence in a sequential setting. This paper also shows that such a failure occurs when we extend the framework of incomplete information games to allow for a representation of uncertainty using sets of probabilities and the use of Gamma-maximin. Nevertheless, the key to this negative result is that a phenomenon called dilation of sets of probabilities obtains in this generalized setting.