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A New Sequence Form Approach For The Enumeration And Refinement Of All Extreme Nash Equilibria For Extensive Form Games

Author

Listed:
  • CHARLES AUDET

    (GERAD and Département de mathématiques et de génie industriel, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montréal (Québec) Canada H3C 3A7, Canada)

  • SLIM BELHAIZA

    (Département de mathmatiques et génie industriel, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montréal (Québec) Canada H3C 3A7, Canada)

  • PIERRE HANSEN

    (GERAD and Méthodes quantitatives de gestion, HEC Montréal, 3000, Chemin de la Côte-Sainte-Catherine, Montréal (Québec) Canada H3T 2A7, Canada)

Abstract

This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequence form of an extensive game is expressed, for the first time to our knowledge, as a parametric linear 0 - 1 program. ConsideringExt(P)as the set of all of the sequence form extreme Nash equilibria andExt(Q)as the set of all the parametric linear 0 - 1 program extreme points, we show thatExt(P) ⊆ Ext(Q). Using exact arithmetics classes, the algorithm EχMIP Belhaiza (2002); Audetet al.(2006) is extended to enumerate all elements ofExt(Q). A small procedure is then applied in order to obtain all elements ofExt(P).

Suggested Citation

  • Charles Audet & Slim Belhaiza & Pierre Hansen, 2009. "A New Sequence Form Approach For The Enumeration And Refinement Of All Extreme Nash Equilibria For Extensive Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 437-451.
    • Handle: RePEc:wsi:igtrxx:v:11:y:2009:i:04:n:s021919890900242x
    DOI: 10.1142/S021919890900242X
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    Cited by:

    1. Rahul Savani & Bernhard Stengel, 2015. "Game Theory Explorer: software for the applied game theorist," Computational Management Science, Springer, vol. 12(1), pages 5-33, January.

    More about this item

    Keywords

    Sequence form; extensive game; Nash equilibrium; extreme equilibrium; enumeration; EχMIP algorithm;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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