#### Date of Original Version

2005

#### Type

Conference Proceeding

#### Abstract or Description

We deﬁne a generalized strategy eliminability criterion for bimatrix games that considers whether a given strategy is eliminable relative to given dominator & eliminee subsets of the players’ strategies. We show that this deﬁnition spans a spectrum of eliminability criteria from strict dominance (when the sets are as small as possible) to Nash equilibrium (when the sets are as large as possible). We show that checking whether a strategy is eliminable according to this criterion is coNPcomplete (both when all the sets are as large as possible and when the dominator sets each have size 1). We then give an alternative deﬁnition of the eliminability criterion and show that it is equivalent using the Minimax Theorem. We show how this alternative deﬁnition can be translated into a mixed integer program of polynomial size with a number of (binary) integer variables equal to the sum of the sizes of the eliminee sets, implying that checking whether a strategy is eliminable according to the criterion can be done in polynomial time, given that the eliminee sets are small. Finally, we study using the criterion for iterated elimination of strategies.

#### Published In

Proceedings of the National Conference on Artificial Intelligence (AAAI).