A NEW SEQUENCE FORM APPROACH FOR THE ENUMERATION AND REFINEMENT OF ALL EXTREME NASH EQUILIBRIA FOR EXTENSIVE FORM GAMES

Charles Audet (), Slim Belhaiza () and Pierre Hansen ()
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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

International Game Theory Review (IGTR), 2009, vol. 11, issue 04, 437-451

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).

Keywords: Sequence form; extensive game; Nash equilibrium; extreme equilibrium; enumeration; EχMIP algorithm (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S021919890900242X

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