Zero Knowledge Games

TL;DR

This paper models zero-knowledge games where players' strategies are non-revealing, emphasizing trust and information concealment, and introduces a linear transformation to analyze common knowledge under public announcements.

Contribution

It introduces a novel framework for zero-knowledge games with non-revealing strategies and a modified sliding-block code for analyzing information flow.

Findings

Zero-knowledge games emphasize trust and soundness.

Players reveal their informed or uninformed status.

The framework supports analysis of strategic trust in game theory.

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.