Admissibility in infinite games

Abstract

We analyse the notion of iterated admissibility, i.e., avoidance of weakly dominated strategies, as a solution concept for extensive games of infinite horizon. This concept is known to provide a valuable criterion for selecting among multiple equilibria and to yield sharp predictions in finite games. However, generalisations to the infinite are inherently problematic, due to unbounded dominance chains and the requirement of transfinite induction. In a multi-player non-zero-sum setting, we show that for infinite extensive games of perfect information with only two possible payoffs (win or lose), the concept of iterated admissibility is sound and robust: all iteration stages are dominated by admissible strategies, the iteration is non-stagnating, and, under regular winning conditions, strategies that survive iterated elimination of dominated strategies form a regular set. © Springer-Verlag Berlin Heidelberg 2007.