Disagreeing About What the Buyer Might Learn

2026-09-27

AI Summary

This study addresses the challenge of evaluating mechanism robustness in bilateral trade when buyers hold divergent beliefs regarding endogenous information signal distributions. By extending the Hansen-Sargent framework to endogenous information acquisition, this work formulates a Bayesian game model subject to $\eta$-entropy ball constraints to characterize worst-case payoffs. The analysis reveals the differential effects of belief divergence on efficient versus inefficient trades: such divergence inflates prices and distorts demand curves. Crucially, when trade may be inefficient, the degree of belief divergence is endogenously amplified conditional on trade occurring. These findings offer novel insights into robust mechanism design under information asymmetry.

Abstract

I introduce a robustness criterion for settings where players may disagree about the distribution over signals induced by endogenously chosen information. In the spirit of Hansen and Sargent (2008), an information choice is evaluated by its worst-case payoff over beliefs within an $\eta$-entropy ball around the signal distribution it induces. I apply this formulation to buyer-optimal learning in bilateral trade (Roesler and Szentes, 2017). If trade is always efficient, disagreement raises the price and twists the buyer's demand curve while preserving full trade. When trade may be inefficient, the same characterization holds conditional on trade with an endogenously amplified disagreement level.

Problem

• robustness criterion
• disagreement
• information choice
• bilateral trade
• buyer-optimal learning

Innovation

• robustness criterion
• eta-entropy ball
• buyer-optimal learning
• bilateral trade
• belief disagreement