Revealed Information

2024-11-20

AI Summary

This paper addresses how an analyst can test whether a decision maker engages in rational information acquisition solely from observed action frequencies—without access to state-contingent data. Specifically, it asks: under what observable conditions can an action distribution be rationalized as arising from optimal information acquisition and Bayesian decision-making given some prior? Method: The authors develop an exact characterization framework based on support functions, deriving a finite system of inequalities that the utility function, prior belief, and action distribution must jointly satisfy. They provide the first complete characterization of the set of consistent posterior beliefs and extend the analysis to continuous action spaces and first-order Bayesian persuasion settings. Contribution: The work delivers necessary and sufficient conditions for the testable implications of rational information structures, enabling comparative statics and modeling of ring-network games. It overcomes a fundamental theoretical bottleneck in identifying rational information behavior from state-unconditional data.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Game Theory and Economic Paradigms: Imperfect Information
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

An analyst observes the frequency with which a decision maker (DM) takes actions, but does not observe the frequency of actions conditional on the payoff-relevant state. We ask when can the analyst rationalize the DM's choices as if the DM first learns something about the state before taking action. We provide a support function characterization of the triples of utility functions, prior beliefs, and (marginal) distributions over actions such that the DM's action distribution is consistent with information given the agent's prior and utility function. Assumptions on the cardinality of the state space and the utility function allow us to refine this characterization, obtaining a sharp system of finitely many inequalities the utility function, prior, and action distribution must satisfy. We apply our characterization to study comparative statics and ring-network games, and to identify conditions under which a data set is consistent with a public information structure in first-order Bayesian persuasion games. We characterize the set of distributions over posterior beliefs that are consistent with the DM's choices. Assuming the first-order approach applies, we extend our results to settings with a continuum of actions and/or states.%

Problem

• Determine when DM's choices reflect state learning
• Characterize utility, prior, action consistency conditions
• Extend results to multi-agent and continuum settings

Innovation

• Support-function characterizes utility, prior, action consistency
• Finitely many inequalities refine utility and prior constraints
• Extends to continuum of actions and multi-agent settings