ISSN:
1432-1270
Schlagwort(e):
Bimatrix game
;
ɛ-equilibrium
;
optimal strategies
;
vertical linear complementarity problem
;
degree
;
stability
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Wirtschaftswissenschaften
Notizen:
Abstract In this article, we consider a two-person game in which the first player picks a row representative matrixM from a nonempty set $$A$$ ofm ×n matrices and a probability distributionx on {1,2,...,m} while the second player picks a column representative matrixN from a nonempty set ℬ ofm ×n matrices and a probability distribution y on 1,2,...,n. This leads to the respective costs ofx t My andx t Ny for these players. We establish the existence of an ɛ-equilibrium for this game under the assumption that $$A$$ and ℬ are bounded. When the sets $$A$$ and ℬ are compact in ℝmxn, the result yields an equilibrium state at which stage no player can decrease his cost by unilaterally changing his row/column selection and probability distribution. The result, when further specialized to singleton sets, reduces to the famous theorem of Nash on bimatrix games.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01254380
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