Heterogeneously Perceived Incentives in Dynamic Environments: Rationalization, Robustness and Unique Selections

TL;DR

This paper explores how differences in agents' perceptions of possible states in dynamic environments influence rationalization, robustness, and the uniqueness of strategic predictions, highlighting the impact of even minor disagreements.

Contribution

It formalizes heterogeneity in agents' perceptions as higher-order disagreements and analyzes their effects on strategic rationalization and prediction robustness.

Findings

Small perception disagreements significantly alter strategic interpretations.

Backward induction predictions are robust to minor perception differences.

Forward induction predictions lack uniqueness and are sensitive to perception heterogeneity.

Abstract

In dynamic settings each economic agent's choices can be revealing of her private information. This elicitation via the rationalization of observable behavior depends each agent's perception of which payoff-relevant contingencies other agents persistently deem as impossible. We formalize the potential heterogeneity of these perceptions as disagreements at higher-orders about the set of payoff states of a dynamic game. We find that apparently negligible disagreements greatly affect how agents interpret information and assess the optimality of subsequent behavior: When knowledge of the state space is only 'almost common', strategic uncertainty may be greater when choices are rationalized than when they are not--forward and backward induction predictions, respectively, and while backward induction predictions are robust to small disagreements about the state space, forward induction predictions are not. We also prove that forward induction predictions always admit unique selections a la Weinstein and Yildiz (2007) (also for spaces not satisfying richness) and backward induction predictions do not.