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Enumeration of all the extreme equilibria in game theory: bimatrix and polymatrix games. (English) Zbl 1122.91009
The autors study the problem of extreme Nash equilibria in bimatrix games and in their special generalization to $$n$$-person games, called polymatrix games . The first obtained result says that such games can be expressed as parametric linear 0-1 programs. Next this is used to construct the $$E\chi$$-MIP algorithm for the complete enumeration of the extreme equilibria in bimatrix and polymatrix games. This algorithm is numeracally illustrated for 3-person polymatrix games of size $$m\times m\times m$$ with $$m$$ up to 13. Also, it is compared with an another EEE algorithm of Audet in computational results on randomly generated bimatrix games for sizes $$n\times n$$ for $$n$$ up to 14.

MSC:
 91A10 Noncooperative games 91A05 2-person games 91A06 $$n$$-person games, $$n>2$$ 91B50 General equilibrium theory
Nash equilibria
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References:
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