Allard, Crispin Toby John (1993) Influence diagrams : a new approach to modelling games. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Game theory, Computer graphics -- Mathematical models
Official Date:	December 1993
Dates:	Date Event December 1993 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Smith, Jim
Sponsors:	Science and Engineering Research Council (Great Britain)
Extent:	vi, 142 leaves : illustrations
Language:	eng

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