Bayesian Games with Intentions

TL;DR

This paper introduces Bayesian games with intentions, a new framework that extends traditional Bayesian and psychological games by distinguishing between intended and actual strategies, enabling richer modeling of belief-dependent preferences.

Contribution

It generalizes Bayesian and psychological games by incorporating intentions, and proves the correspondence of psychological game equilibria within this new framework.

Findings

Bayesian games with intentions can represent a broader class of belief-dependent preferences.

Nash equilibria in psychological games are a special case of equilibria in the proposed framework.

The framework bridges the gap between Bayesian and psychological game models.

Abstract

We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games, and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.