State Information in Bayesian Games

TL;DR

This paper explores how transmitting state information to a player in Bayesian games affects optimal performance, highlighting the role of communication rates and randomization in strategic decision-making.

Contribution

It introduces a framework for understanding the impact of helper-transmitted state information on Bayesian game outcomes, emphasizing the importance of communication strategies.

Findings

Higher communication rates enable more effective randomization in strategies.

Transmitting state information can significantly alter game value and strategies.

Encoding for adversarial settings differs from traditional rate-distortion approaches.

Abstract

Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the resulting value of the game has been analyzed under the framework of Bayesian games. This investigation considers the optimal performance in a game when a helper is transmitting state information to one of the players. Encoding information for an adversarial setting (game) requires a different result than rate-distortion theory provides. Game theory has accentuated the importance of randomization (mixed strategy), which does not find a significant role in most communication modems and source coding codecs. Higher rates of communication, used in the right way, allow the message to include the necessary random component useful in games.