Strategic Behavior under Context Misalignment

TL;DR

This paper explores how misaligned beliefs in dynamic games influence strategic behavior under rationality assumptions, revealing potential inconsistencies with traditional belief-based analyses.

Contribution

It introduces the notion of separating type structures to distinguish real and imaginary belief hierarchies, extending RCSBR analysis to account for belief misalignment.

Findings

Misalignment of beliefs can lead to behavioral predictions inconsistent with standard RCSBR.

Dynamic games exhibit different reasoning patterns compared to static games under belief misalignment.

The framework characterizes real types' behavior across all separating type structures.

Abstract

We study the behavioral implications of Rationality and Common Strong Belief in Rationality (RCSBR) with contextual assumptions allowing players to entertain misaligned beliefs, i.e., players can hold beliefs concerning their opponents' beliefs where there is no opponent holding those very beliefs. Taking the analysts' perspective, we distinguish the infinite hierarchies of beliefs actually held by players ("real types") from those that are a byproduct of players' hierarchies ("imaginary types") by introducing the notion of separating type structure. We characterize the behavioral implications of RCSBR for the real types across all separating type structures via a family of subsets of Full Strong Best-Reply Sets of Battigalli & Friedenberg (2012). By allowing misalignment, in dynamic games we can obtain behavioral predictions inconsistent with RCSBR (in the standard framework), contrary to the case of belief-based analyses for static games--a difference due to the dichotomy "non-monotonic vs. monotonic" reasoning.