A Graphical method for simplifying Bayesian Games

TL;DR

This paper introduces a graphical method using chain event graphs to simplify asymmetric Bayesian games, enabling players to deduce optimal strategies more efficiently in complex, asymmetric scenarios.

Contribution

It presents a novel application of chain event graphs for simplifying Bayesian games with asymmetry, extending the utility of graphical models in game theory.

Findings

Chain event graphs enable simplification of complex Bayesian games.

Players can deduce optimal policies using CEGs assuming common knowledge of topology.

The method is demonstrated through a real-world example involving government and radicalization.

Abstract

If the influence diagram (ID) depicting a Bayesian game is common knowledge to its players then additional assumptions may allow the players to make use of its embodied irrelevance statements. They can then use these to discover a simpler game which still embodies both their optimal decision policies. However the impact of this result has been rather limited because many common Bayesian games do not exhibit sufficient symmetry to be fully and efficiently represented by an ID. The tree-based chain event graph (CEG) has been developed specifically for such asymmetric problems. By using these graphs rational players can make analogous deductions, assuming the topology of the CEG as common knowledge. In this paper we describe these powerful new techniques and illustrate them through an example modelling a game played between a government department and the provider of a website designed to radicalise vulnerable people.