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

Abstract

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.

Acknowledgements

I am indebted to my dissertation committee for valuable suggestions and guidance: John Dickhaut (Chair), Beth Allen, Chandra Kanodia, and Gregory Waymire. I wish to thank Ron King, Christian Leuz, Harry Evans, Jack Stecher, Regina Anctil, associate editor John Christensen, and two anonymous referees for helpful comments and suggestions. I also wish to thank workshop participants at the London School of Economics, the Indian School of Business, the University of Pittsburgh, Argyros School of Business and Economics (Chapman University), the University of Toronto, the University of Alberta, and the Economic Science Institute (Chapman University); and referees for the National Science Foundation Doctoral Dissertation Grant and for the University of Minnesota Graduate School Fellowship; and various conference participants. I gratefully acknowledge support from National Science Foundation Doctoral Dissertation Grant Number 0820455 and from Accounting Research Center at Carlson School of Management, University of Minnesota.

Notes

^†This paper is based on my PhD dissertation at the University of Minnesota.

Note that this idea can also be captured by expanding the set of k_t to include more elements than the ones specified here. The equilibrium and other results derived will be qualitatively similar. The set of k_t used here is the most parsimonious one possible.

If δ ≤ (4/(l + h)) ⁿ , the investor will not invest, making the rational manager indifferent between d ₁ = 0 and d ₁ = 1.

Additional information

Notes on contributors

Radhika Lunawat

Paper accepted by John Christensen.