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Title: Influence diagrams : a new approach to modelling games
Author: Allard, Crispin Toby John
ISNI:       0000 0001 3415 1075
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1993
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Game theory seeks to describe the interaction of two or more actors with distinct objectives. This is achieved using a mathematical model known as a game. Virtually all game theory relies on either the extensive form or the normal form to represent the games being studied. By drawing on the previously unrelated fields of game theory and graphical modelling, and by taking a new approach to the way in which a game is modelled, an alternative to the extensive and normal forms is developed: the belief influence diagram (BID). Starting from the basic definition of a game and using a new form of conditional belief called a prospective function, it is shown how the decision influence diagram can be adapted to model games. The advantages of the BID over the extensive and normal forms are explored, particularly its ability to model some of the qualitative aspects of games and to model games of greater complexity. By using BIDs in the modelling of games, fresh insight can be gained into certain features of the game, such as what sources of information an actor in the game should take account of. New concepts of sufficiency and parsimony are defined which relate to the BID. It is shown how these concepts, when combined with different forms of rationality, can lead to a variety of methods for simplifying a BID, and hence simplifying the game which it represents. It is shown that such simplifications arc invariant with respect to the order in which the simplifying steps are carried out. A schematic version of the BID is used to model finite repeated games and to develop concepts of learning and local sufficiency. It is shown how BIDs can be used to facilitate an induction proof in a finite repeated game and to model a highly complex competitive market. This last example is used to illustrate how BIDs can be helpful in evaluating some qualitative aspects of a model.
Supervisor: Not available Sponsor: Science and Engineering Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics