Limited belief propagation and contingent thinking

2026-06-09

AI Summary

This study addresses failures in conditional reasoning, neglect of relevance, and violations of iterated expectations that arise when agents operate under partial observability and limited inference depth. To account for these cognitive biases, the authors propose a finite belief propagation framework, which formalizes such limitations as asymmetries in reasoning depth for the first time. The model, grounded in directed acyclic graphs, differentiates between inference processes over observed and unobserved variables and integrates both Bayesian and non-Bayesian updating criteria. Validated through behavioral experiments and strategic settings—including public goods provision and social learning—the framework not only explains established findings in conditional reasoning but also demonstrates how bounded inference systematically shapes economic decision-making.

Abstract

An agent updates her beliefs over a set of variables after observing some of them. We provide a representation of updated beliefs that captures limited propagation of her observation's implications through the directed acyclic graph that represents the relations between all variables. Failure of contingent thinking occurs when she performs fewer inference steps from unobserved variables than observed ones, leading to correlation neglect and violations of iterated expectations. Our framework offers a new perspective on existing experiments about contingent thinking and suggests new directions. We characterize the model's relationship with familiar Bayesian and non-Bayesian benchmarks, and illustrate it with applications to public-good provision and social learning games.

Problem

• belief updating
• contingent thinking
• limited inference
• correlation neglect
• iterated expectations

Innovation

• limited belief propagation
• contingent thinking
• directed acyclic graph
• correlation neglect
• iterated expectations