Zero Knowledge Games

Abstract

In this paper we model a game such that all strategies are non-revealing, with imperfect recall and incomplete information. We also introduce a modified sliding-block code as a linear transformation which generates common knowledge of how informed a player is under public announcements. Ultimately, we see that between two players or two coalitions; zero-knowledge games where both players are informed have the utility of trust established in the mixed strategy Nash equilibrium. A zero-knowledge game is one of trust and soundness, placing utility in being informed. For any player who may be uninformed, such players reveal they are uninformed. The "will to verify" may be eroded such that the claimant is never held responsible for their repeated false claims or being uninformed.