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Toward a Generic Mathematical Model of Abstract Game Theories

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Transactions on Computational Science II

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5150))

Abstract

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

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Authors and Affiliations

  1. Theoretical and Empirical Software Engineering Research Centre (TESERC) International Center for Cognitive Informatics (ICfCI) Dept. of Electrical and Computer Engineering Schulich School of Engineering, University of Calgary, 2500 University Drive, NW, Calgary, Alberta, T2N 1N4, Canada

    Yingxu Wang

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  1. Yingxu Wang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, AB, Canada

    Marina L. Gavrilova

  2. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  3. Schulich School of Engineering, Department of Electrical and Computer Engineering, University of Calgary, 2500 University Drive, T2N 1N4, NW Calgary, AB, Canada

    Yingxu Wang

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. School of Information Science & Technology, Southwest Jiaotong University, 610031, Chengdu, China

    Guoyin Wang

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Wang, Y. (2008). Toward a Generic Mathematical Model of Abstract Game Theories. In: Gavrilova, M.L., Tan, C.J.K., Wang, Y., Yao, Y., Wang, G. (eds) Transactions on Computational Science II. Lecture Notes in Computer Science, vol 5150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87563-5_12

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  • DOI: https://doi.org/10.1007/978-3-540-87563-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87562-8

  • Online ISBN: 978-3-540-87563-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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