The Role of Information in Building Reputation in an Investment/Trust Game

Abstract

This article analyzes the role of information in building reputation in an investment/trust game. The model allows for information asymmetry in a finitely repeated sender-receiver game and solves for sequential equilibrium to show that if there are some trustworthy managers who always disclose their private information and choose to return a fair proportion of the firm’s income as dividend to the investor, then a rational manager will mimic such behaviour in an attempt to earn a reputation for being trustworthy. The rational manager will mimic with probability 1 in the early periods of the game. The investor, too, will invest with probability 1 in these periods. However, in the later periods, the rational manager will mimic with a certain probability strictly less than 1. The probability will be such that it will make the investor indifferent between investing and not investing, and he, in turn, will invest with a probability (strictly less than 1) that will make the rational manager indifferent between mimicking and not mimicking; that is, the game will begin with pure strategy play but will switch to mixed strategy play. There is one exception, though: when the investor’s ex ante beliefs about the manager’s trustworthiness are exceptionally high, the game will continue in a pure strategy, and the switch to mixed strategy play will never occur. Identical results obtain if the manager’s choice of whether to share his private information with the investor is replaced by exogenously imposed information sharing.

Keywords: Information, Disclosure, Reputation, Trust

JEL Classification: M41, D82, C11, C73.