Asymmetric Rationality: Protocol Design and Behavioral Anomalies

Abstract

We study how asymmetric rationality in strategic interactions can generate seemingly anomalous patterns of belief updating and behavior. A boundedly rational receiver designs a finite-state decision protocol to learn from a fully rational, privately informed, and biased sender who controls the flow of information. The receiver must allocate scarce memory between learning and incentive provision. We identify a simple class of protocols sufficient for optimal design and show how their structure generates information disengagement, indecision, and polarization. The receiver hesitates before deciding but becomes unresponsive to further evidence afterward. Identical receivers following the same protocol can reach opposing decisions despite receiving the same sequence of signals, with the probability of disagreement remaining bounded away from zero as their payoffs approach the optimum. These behaviors, which might otherwise appear erratic or psychologically driven, arise from the strategic use of limited memory.