Toward a generic mathematical model of abstract game theories

Authors:
Yingxu Wang
Affiliations:
Theoretical and Empirical Software Engineering Research Centre, International Center for Cognitive Informatics, Dept. of Electrical and Computer Engineering, Schulich School of Engineering, Univer ...
Venue:
Transactions on computational science II
Year:
2008

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Abstract

Games are a complex mathematical structure for modeling dynamicdecision processes under competition where opponent players compete for themaximum gain or toward a success state in the same environment according tothe same rules of the game. Games are conventionally dealt with payoff tablesbased on random strategies, which are found inadequate to describe the dynamicbehaviors of games and to rigorously predict the outcomes of games.This paper presents an abstract game theory, which enables a formal treatmentof games by a set of mathematical models for both the layouts and behaviors ofgames. A generic mathematical model of abstract games is introduced, based onwhich the properties of games in terms of decision strategies and serial matchesare described. A wide range of generic zero-sum and nonzero-sum games areformally modeled and analyzed using the generic mathematical models of abstractgames.