We prove that an equilibrium of a nondegenerate bimatrix game has index +∈1 if and only if it can be made the unique equilibrium of an extended game with additional strategies of one player. The main tool is the "dual construction". A simplicial polytope, dual to the common best-response polytope of one player, has its facets subdivided into best-response regions, so that equilibria are completely labeled points on the surface of that polytope. That surface has dimension m∈-∈1 for an m×n game, which is much lower than the dimension m∈+∈n of the polytopes that are classically used. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Von Schemde, A., & Von Stengel, B. (2008). Strategic characterization of the index of an equilibrium. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4997 LNCS, pp. 242–254). https://doi.org/10.1007/978-3-540-79309-0_22
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