A Note on Bayesian Rationality and Correlated Equilibrium

TL;DR

This paper examines the limitations of Bayesian rationality in strategic games with imperfect information, showing that strategic independence depends on strategic uncertainty, which impacts the understanding of equilibrium solutions.

Contribution

It reveals that Bayesian rationality assumptions are violated in games with imperfect information and clarifies the role of strategic uncertainty in equilibrium concepts.

Findings

Bayesian rationality is violated in all games with imperfect information.

Strategic independence requires the presence of strategic uncertainty.

Distinguishing between strategic certainty and uncertainty explains different Prisoner's Dilemma solutions.

Abstract

Bayesian rationality in strategic games presumes that it is possible to translate strategic uncertainty into imperfect information. Correlated equilibrium is guided by the idea that players are Bayes rational, have a common prior, and choose their strategies independently. I show that an essential condition for Bayesian rationality is violated in every game with imperfect information. Moreover, without strategic uncertainty, players cannot choose their strategies independently. This means strategic independence requires strategic uncertainty. If we distinguish between strategic certainty and uncertainty, we are able to explain both the existence of the cooperative and the noncooperative solution of the prisoner's dilemma.