Causal Games and Causal Nash Equilibrium

TL;DR

This paper introduces causal games, extending classical game theory to include causal information and proposing a new belief updating method for Bayesian games with unknown causal models, leading to a new concept of causal Nash equilibrium.

Contribution

It defines causal decision problems and causal games, and develops a probability updating method for Bayesian games with unknown causal models, introducing causal Nash equilibrium.

Findings

Proposed a new belief updating method for causal Bayesian games.

Defined causal Nash equilibrium for strategic games with causal information.

Extended classical game theory to incorporate causal models and decision-making.

Abstract

Classical results of Decision Theory, and its extension to a multi-agent setting: Game Theory, operate only at the associative level of information; this is, classical decision makers only take into account probabilities of events; we go one step further and consider causal information: in this work, we define Causal Decision Problems and extend them to a multi-agent decision problem, which we call a causal game. For such games, we study belief updating in a class of strategic games in which any player's action causes some consequence via a causal model, which is unknown by all players; for this reason, the most suitable model is Harsanyi's Bayesian Game. We propose a probability updating for the Bayesian Game in such a way that the knowledge of any player in terms of probabilistic beliefs about the causal model, as well as what is caused by her actions as well as the actions of every other player are taken into account. Based on such probability updating we define a Nash equilibria for Causal Games.