The Role of Monotonicity in the Epistemic Analysis of Strategic Games

TL;DR

This paper explores how monotonicity affects the analysis of rational strategies in strategic games, extending classical results to more general settings using Tarski's Fixpoint Theorem.

Contribution

It provides a general theorem linking monotonic rationality notions with iterative elimination processes in strategic games, broadening the scope of classical results.

Findings

Monotonic rationality notions lead to stronger elimination results.

Theorem applies to arbitrary games and transfinite iterations.

Clarifies limitations for non-monotonic dominance notions.

Abstract

It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski's Fixpoint Theorem.