Cryptographically Blinded Games: Leveraging Players' Limitations for Equilibria and Profit

Abstract: In this work we apply methods from cryptography to enable any number of mutually distrusting players to implement broad classes of mediated equilibria of strategic games without the need for trusted mediation. Our implementation makes use of a (standard) pre-play "cheap talk" phase, in which players engage in free and non-binding communication prior to playing in the original game. In our cheap talk phase, the players execute a secure multi-party computation protocol to sample an action profile from an equilibrium of a "cryptographically blinded" version of the original game, in which actions are encrypted. The essence of our approach is to exploit the power of encryption to selectively restrict the information available to players about sampled action profiles, such that these desirable equilibria can be stably achieved. In contrast to previous applications of cryptography to game theory, this work is the first to employ the paradigm of using encryption to allow players to benefit from hiding information \emph{from themselves}, rather than from others; and we stress that rational players would \emph{choose} to hide the information from themselves.