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Testing Information Ordering for Strategic Agents

Sukjin Han, Hiroaki Kaido, Lorenzo Magnolfi

TL;DR

This paper develops a BCE-based framework to test whether the true information structure in a strategic discrete game is at least as informative as a chosen baseline, avoiding strong parametric assumptions about the information environment. It translates information-ordering into moment inequalities via the BCE prediction set $Q_{ heta,S^r}^{ ext{BCE}}(x)$ and implements a bootstrap procedure to achieve uniform asymptotic validity, including extensions for multiple hypotheses and market-level confidence sets. The authors illustrate the method with a Monte Carlo exercise and an empirical application to airline markets, finding evidence against the privileged-information hypothesis—especially in large, competitive markets—suggesting hub status does not confer systematic informational advantages beyond cost and demand benefits. The approach provides a general, nonparametric tool for detecting information asymmetries in strategic contexts, with important implications for counterfactual policy and empirical research where information structure is uncertain or difficult to specify precisely.

Abstract

Specifying the information structure in strategic environments is difficult for empirical researchers. We develop a test of information ordering that examines whether the true information structure is at least as informative as a proposed baseline. Using Bayes Correlated Equilibrium (BCE), we translate the ordering of information structures into testable moment inequalities and establish uniform asymptotic validity for our testing procedure. In an application to U.S. airline markets, we test whether hub airlines have informational advantages beyond cost and demand benefits. We reject the privileged information hypothesis, with rejections concentrated in large, competitive markets.

Testing Information Ordering for Strategic Agents

TL;DR

This paper develops a BCE-based framework to test whether the true information structure in a strategic discrete game is at least as informative as a chosen baseline, avoiding strong parametric assumptions about the information environment. It translates information-ordering into moment inequalities via the BCE prediction set and implements a bootstrap procedure to achieve uniform asymptotic validity, including extensions for multiple hypotheses and market-level confidence sets. The authors illustrate the method with a Monte Carlo exercise and an empirical application to airline markets, finding evidence against the privileged-information hypothesis—especially in large, competitive markets—suggesting hub status does not confer systematic informational advantages beyond cost and demand benefits. The approach provides a general, nonparametric tool for detecting information asymmetries in strategic contexts, with important implications for counterfactual policy and empirical research where information structure is uncertain or difficult to specify precisely.

Abstract

Specifying the information structure in strategic environments is difficult for empirical researchers. We develop a test of information ordering that examines whether the true information structure is at least as informative as a proposed baseline. Using Bayes Correlated Equilibrium (BCE), we translate the ordering of information structures into testable moment inequalities and establish uniform asymptotic validity for our testing procedure. In an application to U.S. airline markets, we test whether hub airlines have informational advantages beyond cost and demand benefits. We reject the privileged information hypothesis, with rejections concentrated in large, competitive markets.
Paper Structure (31 sections, 15 theorems, 158 equations, 2 figures, 3 tables, 1 algorithm)

This paper contains 31 sections, 15 theorems, 158 equations, 2 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Model
  3. Payoff Structure and Information Structure
  4. Equilibrium and Predictions
  5. Comparing Information Structures
  6. Tests of Information Ordering
  7. Equilibrium Concept and Predictions Robust to Information Specification
  8. Testable Implications
  9. Test Statistics and Asymptotic Properties
  10. Computational Aspects
  11. Extensions
  12. Testing Multiple Hypotheses with a Sequence of Baselines
  13. Confidence Sets for Markets with a Specified Baseline
  14. Monte Carlo Experiments
  15. Simulation Design
  16. ...and 16 more sections

Key Result

Lemma 1

For any baseline information structure $S_B$, we let the set of information structures $\mathcal{S}^{*}(S_B)$ be the subset of $\mathcal{S}(S_B)$ such that any two $S, S^{\prime}\in \mathcal{S}^{*}(S_B)$ have a different canonical representation. Then, for any $S,S'\in \mathcal{S}^*(S_B)$, $S\succeq

Figures (2)

  • Figure 1: Equilibrium CCPs and the BCE Prediction
  • Figure 2: Rejection Probability of the Test

Theorems & Definitions (39)

  • Example 1
  • Definition 1: Bayes Nash Equilibrium
  • Definition 2: BNE Predictions
  • Definition 3: Combination
  • Definition 4: Expansion
  • Definition 5: Set of Expansions
  • Definition 6: Individual Sufficiency
  • Definition 7
  • Remark 1
  • Lemma 1
  • ...and 29 more