Trust and reputation under asymmetric information☆
Introduction
Trust is an important condition for bilateral and informal trade that cannot be undertaken under formal contracts. For a potentially welfare-improving trade to take place, one party must choose to trust the other by, for example, lending money, delegating tasks, or exerting effort in a project. If the probability that the money lent will be paid back, that tasks will be well executed, or that effort will be rewarded by bonuses is high enough, trusting the other party is part of an equilibrium. In many real-world applications, it seems reasonable to assume that an entrepreneur who receives an investment is better informed about the value of his business than an investor lending money. Given the importance of trust in many bilateral interactions, it is of value to investigate how such informational asymmetries influence the possibility that trust will thrive.
In this paper, we study a finitely repeated investment game (Berg et al., 1995). Typically, in such a game, an investor sends a sum of money to a ’trustee’ and, along the way, this money is multiplied by a commonly known factor (henceforth multiplier). Out of the money received, the trustee chooses how much to send back to the investor. We assume different types of trustees: a trustworthy type who always returns to the investor at least the amount that she sent to him, and a strategic type who maximizes his expected payoff. The strategic trustee builds up his reputation by mimicking the behavior of the trustworthy type. Several papers have tested this equilibrium prediction in a laboratory experiment, with varying results (e.g. Camerer, Weigelt, 1988, Neral, Ochs, 1992, Anderhub, Engelmann, Güth, 2002). A change in information about the value of the multiplier has so far been largely overlooked despite the abundance of economic interactions characterized by asymmetric information.
The value of the multiplier determines whether a strategic trustee has an interest in building up their reputation or whether he is only interested in immediate gains. To study how information about the multiplier affects trust and repayments we compare two versions of the game, one in which the multiplier is common knowledge (Public regime) and another in which it is private information known only to the trustee (Private regime).
We consider the following game between an Investor and an Entrepreneur. The Investor decides in every period whether or not to trust an Entrepreneur by investing a fixed amount in his project. The Entrepreneur is one of two types, a good type who always repays loans, or a strategic type who is an expected-payoff maximizer. At the beginning of the game, the strategic type observes the value of a multiplier which tells by how much each unit invested grows in the hands of the Entrepreneur. Hence, the multiplier represents the revenue from one unit of investment. The value of the multiplier remains unchanged throughout the game and, in every equilibrium, the multiplier determines whether or not the Entrepreneur has an incentive to build his reputation by repaying early investments. If the revenue is not high enough to cover the costs of capital, a strategic Entrepreneur is assumed to abandon his project. When the contracted relationship between the Investor and Entrepreneur is informal, this decision would lead him to default on the Investor’s loan. Thus, in equilibrium, knowledge of the multiplier allows the Investor to know what the motivations of the strategic Entrepreneur are. When the multiplier is not known to the Investor, there is additional uncertainty. Not only is the type of Entrepreneur unknown, but so is the incentive to invest in their reputation, which is non-observable to the Investor.
Our theoretical analysis shows that there are perfect Bayesian equilibria where there are mixed strategies for a large range of parameters. The mixed strategy perfect Bayesian equilibrium predicts that the ex-ante frequency of investments and repayments is higher when the Investor is uncertain about the motivations of a strategic Entrepreneur (Private regime). The underlying mechanism is that mixing between investing and not investing starts in a later period in the case of additional uncertainty. A direct implication of this result is that in the mixed-strategy equilibrium both the Investor and the strategic Entrepreneur obtain a higher expected payoff under the Private regime.
We run a laboratory experiment to test whether this perfect Bayesian equilibrium is selected by subjects and how subjects behave under the different information regimes. The results do not confirm the Bayesian theoretical prediction of more investments under private information about the multiplier. We discuss potential reasons for the deviations between theoretical prediction and behavior in the experiment. While including risk aversion to the model cannot lead to the observed behavior, a publicly known share of entrepreneurs who repay an investment even though it leads to monetary losses could explain the observed data. We can show that such behavior occurs to a large extent and is highly correlated with a proxy of a subject’s cognitive ability.
The remainder of the paper is organized as follows. Section 2 summarizes the related literature. Section 3 formalizes the model. Section 4 outlines the model’s perfect Bayesian equilibrium, for public and private knowledge about the payoff multiplier; forms predictions about the numerical example tested in the laboratory; and indicates the welfare implications under the different regimes. Sections 5 and 6 present the experiment, its results and explores on reasons for deviating findings. Section 7 discusses and concludes.
Section snippets
Literature
Since Berg et al. (1995), a vast literature in behavioral economics has studied variants of the trust game between a trustor and a trustee in the lab. Camerer (2003) offers a survey of these studies which have consistently found that, against theoretical predictions, people tend to reciprocate trust even in one-shot interactions. More importantly, numerous studies, such as Anderhub et al. (2002); Neral and Ochs (1992); Camerer and Weigelt (1988) and Brandts and Figueras (2003), have
The game
The structure of the game is shown in Fig. 1. Player A (Investor) and Player B (Entrepreneur) interact over a finite and commonly known number of rounds, . In every round, an Investor can choose whether or not to invest the fixed amount .1 The Entrepreneur can be one of two types: . A good Entrepreneur cannot default on an investment at any point in the game. A bad Entrepreneur can decide in each round whether to
Equilibrium predictions
The game is solved theoretically using the concept of perfect Bayesian equilibria (PBE), where the actions and beliefs of the two players correspond and best-react to each other. We define the probability of investment, and the probability of repayment in period given history of play up to period . denotes the updated belief of the Investor about the probability that the Entrepreneur is in period given history of play, . Hence, denotes the
Experimental design and procedure
To test to what extent the perfect Bayesian equilibrium can explain actual behavior we conducted a laboratory experiment.
The multiplier the type of Entrepreneur (good or bad) and the regime (Public or Private) is varied within subjects. The probability of being a good Entrepreneur, is varied between subjects. At the beginning of each round, this share randomly (and independently of the other Entrepreneurs’ outcomes) determines the type of an Entrepreneur. Each round
Efficiency and regime choice
In the PBE equilibrium, the (theoretical) welfare dominance of Private compared to Public stems from the higher probability of investing up to the last period of a game. Under the Public regime, due to mixing, there is a higher risk that the game will end abruptly, which leads to unrealized expected gains. To test the overall effect of regime, we estimate the probability of having an investment in the third (final) period (Table 3). The regression does not use all data stemming from the
Discussion and conclusion
Our aim in this paper has been to study the effect of information about the multiplier on trust and repayments. Therefore, we have chosen to keep the model as close to the “standard” trust game as possible. Thus, despite the labels we use, the model is not intended to be a realistic model of investment behavior. However, with small changes and adjustments, the model could be shaped to better represent an actual investment game, without significant changes to the qualitative results. For
Declaration of Competing Interest
Declarations of interest: none
References (19)
- et al.
An experimental study of the repeated trust game with incomplete information
J. Econ. Behav. Organ.
(2002) - et al.
Trust, reciprocity, and social history
Games Econ. Behav.
(1995) When social outcomes aren’t fair: the effect of causal attributions on preferences
Organ. Behav. Hum. Decis. Process.
(1995)- et al.
An exploration of reputation formation in experimental games
J. Econ. Behav. Organ.
(2003) - et al.
Reputation and imperfect information
J. Econ. Theory
(1982) An experimental investigation of reputation effects of disclosure in an investment/trust game
J. Econ. Behav. Organ.
(2013)Reputation effects of information sharing
J. Econ. Behav. Organ.
(2016)Starting small and renegotiation
J. Econ. Theory
(1999)Starting small and commitment
Games Econ. Behav.
(2002)
Cited by (2)
- ☆
We would like to thank Urs Fischbacher, Susanne Goldlücke, Juuso Välimäki, the TWI research group, the anonymous referees, the Associate Editor and the Editor, as well as participants at several workshops and conferences for valuable comments. All remaining errors are our own. The work was supported by University of Konstanz funds.