A New Sequence Form Approach for the Enumeration and Refinement of All Extreme Nash Equilibria for Extensive Form Games

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. Considering Ext(P ) as the set of all of the sequence form extreme Nash equilibria and Ext(Q) as the set of all the parametric linear 0 − 1 program extreme points, we show that Ext(P ) ⊆ Ext(Q). Using exact arithmetics classes, the algorithm EχMIP Belhaiza (2002); Audet et al. (2006) is extended to enumerate all elements of Ext(Q). A small procedure is then applied in order to obtain all elements of Ext(P ).