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

This article analyses 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.