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Paper No. 11-20

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PA Thwaites and JQ Smith

A graphical method for simplifying Bayesian games

Date: May 2011

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, and new separation theorems for these graphs make it possible for rational players to 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 risks to electronic communciation.

Keywords: Bayesian game theory, chain event graph, decision tree, influence diagram, parismony.