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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: A New Graphical approach to Bayesian Games

Presented by Peter Thwaites, University of Leeds

20 November 2017 14:00 in CM221

Many Bayesian games can be readily represented by graphical structures such as MAIDS
(Multi-agent influence diagrams). But the development of these representations has coincided
with concerns expressed regarding the application of Bayesian game theory to real
problems. This talk focuses on two of these concerns. Firstly, a player may assume that
an opponent is subjective expected utility maximizing (SEUM), but in many real games it is
improbable that they can know the exact quantitative form of this opponent’s utility function.
Secondly, many common Bayesian games have highly asymmetric game trees, and cannot
be fully or efficiently represented by a MAID.
To address these concerns we suggest the use of CEGs (Chain Event Graphs). These
were introduced in 2008 (Smith & Anderson, Artificial Intelligence) for the modelling of
probabilistic problems exhibiting significant asymmetry. They encode the conditional independence/
Markov structure of these problems completely through their topology, and have
been successfully used for both causal and decision analysis. We show here how causal
CEGs can be used to model asymmetric games. The players know the structure of the game,
but not the exact forms of other players’ utilities, and are SEUM conditioned on the information
available to them each time they make a decision. This means our solution technique
does not in general compute subgame perfect Nash equilibria, but the solutions reached will
be those that each player believes exists. We illustrate our ideas with an example of a game
between a government department and a group trying to radicalise members of the population.
The work in this talk is described in more detail in Thwaites & Smith: A graphical
method for simplifying Bayesian Games, Reliability Engineering and System Safety, 2017.

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