The Study of a Mathematical Model in Information Acquisition and Disclosure

Ce Huang

doi:10.1155/2015/491328

Abstract

A mathematical model involving a decision maker and an expert is investigated. Through analyzing the model, we obtain several results on the expert’s information acquisition and disclosure strategy. When withholding information is costly to the expert, in equilibrium, an expert with a higher withholding cost acquires less information but discloses more acquired information. We also examine which expert is optimal to the decision maker among a group of experts with different costs of withholding information.

Highlights

In many situations, a decision maker needs to make a decision but does not know which decision is the best one
We examine which expert is optimal to the decision maker among a group of experts with different costs of withholding information
The decision maker often looks for advice from investment consultants or doctors, who are experts and are better informed

Summary

Introduction

A decision maker needs to make a decision but does not know which decision is the best one. The equilibrium concept is perfect Bayesian Nash equilibrium (hereafter “the equilibrium”) It consists of three components: the expert’s strategy in how much effort to exert in acquiring information about the state and which states to be disclosed to DM after observing the state; DM’s strategy in what decision to be taken when the expert does not disclose information; and DM’s belief about the state when the expert does not disclose information. We consider how much effort the expert will exert in information acquisition, given DM’s decision in the event of nondisclosure, aφ, and the expert’s optimal information disclosing strategy derived above. When information about the state is obtained, the expert withholds information if and only if the observed θ is lower than a cutoff value k (given the expert’s utility function, any equilibrium strategy in information disclosure must have this “cutoff ” property). We suppress the dependence of these equilibrium variables on x in order to keep notations simple

Equilibrium Characterization

Optimal Expert

An Alternative Utility Function of Expert

Conclusion