Zero Knowledge Games
This work addresses trust and soundness issues in game theory for scenarios with incomplete information, though it appears incremental in extending existing concepts.
The paper tackles the problem of modeling games where strategies are non-revealing with imperfect recall and incomplete information, resulting in a framework where zero-knowledge games establish trust in mixed strategy Nash equilibria, with informed players gaining utility and uninformed players revealing their lack of information.
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.