Are People Sometimes Too Honest? Increasing, Decreasing, and Negative Returns to Honesty.

• Author: Basuchoudhary, Atin

Atin Basuchoudhary [*]

John R. Conlon [+]

We show that sender honesty can hurt receivers in simple signaling games. The receiver faces a trade-off between its ability to work with senders and the quality of information it can get and use from them. Our example also contradicts recent work suggesting that returns to honesty should be increasing. Positive, increasing returns are restored in our model if the receiver can precommit.

1. Introduction

   Ordinary intuition suggests that we prefer to deal with honest people (Sobel 1985). Honest people give reliable information, so we can act on that information with confidence. [1] This paper explores the limits of this intuition in the context of a simple signaling game. In this game, contrary to intuition, the receiver's expected payoff decreases in the probability that the sender is honest.

   The example we consider involves an employee (sender) who must decide whether to go to a mentor/supervisor (receiver) for advice. The supervisor is more experienced than the employee and so will be able to help the employee solve the problem. However, if the supervisor thinks that the problem is big, she may investigate in order to assign blame for the problem.

   Thus, an employee with a big problem may be reluctant to go to the supervisor for advice. If the employee is dishonest, he may be able to conceal the true magnitude of the problem while still benefitting from the supervisor's advice. [2] However, an honest employee with a big problem may not want to go to the supervisor since, if he goes, he will always reveal the true magnitude of the problem. [3] Since the supervisor wants all employees with problems to come to her for advice, she may therefore be hurt by the presence of honest employees, whose problems remain unsolved because they do not get the benefit of her experience and so are less able to resolve their problems. [4]

   This reasoning can be extended to a number of public health applications. Organizations that combat AIDS are often faced with at-risk people who engage in illegal activities (e.g., intravenous drug users or prostitutes). These organizations want at-risk people to reveal their types and use services (like provision of clean syringes or condoms) that may help reduce the risk of AIDS. However, at-risk people may fear that the health agency will reveal compromising information to law enforcement authorities. This may deter at-risk people from truthful revelation. Thus, if at-risk people are honest, or for some other reason have difficulty concealing their illegal behavior from the organization, then they may choose not to use the services of the organization at all.

   Similarly, victims of domestic violence may need to go to a hospital emergency room (ER) for the treatment of injuries from the abuse. The ER personnel would like to ask the source of the injury and encourage the victim to go to a domestic violence center for long-term help. However, the victim may be unwilling to face the embarrassment of questioning. To avoid these questions, victims who are uncomfortable finding evasive answers may choose not to go to the hospital for treatment.

   The provision of contraceptives in schools presents a similar problem. Sexually active teens with many sexual partners may be especially embarrassed to approach the school nurse for contraceptives. Honest but promiscuous teenagers may prefer unprotected sex rather than admit they have many partners.

   There may be negative returns to honesty in other situations as well. For example, potential survey respondents may not be certain about the confidentiality of their responses. If certain questions are especially embarrassing, then honest respondents may choose not to participate in the survey at all rather than answer the embarrassing questions truthfully. Thus, embarrassing questions could lead to sample selection bias for all questions on the survey. An increase in the number of honest potential respondents could therefore lead to less accurate information being collected by the survey.

   This phenomenon will arise whenever people have difficulty in hiding compromising behavior, regardless of their actual honesty; that is, any sender who cannot hide compromising issues from the receiver may avoid the receiver altogether. This avoidance may hurt the receiver.

   Many organizations, however, understand the need for this kind of confidentiality. They therefore try to commit themselves to respect the sender's confidentiality so senders feel safe coining to them.

   This suggests, paradoxically, that the receiver should commit herself to ignoring certain types of useful information. In the example we use for illustration, the supervisor can do better if she commits herself to not attach blame for problems, or, if blame is attached, to not discipline the employee too harshly. Section 4 suggests that returns to the supervisor from employee honesty will generally be positive if the receiver can precommit herself in this way.

   Our example is also interesting because the receiver's expected payoff fails to be convex in probabilities of sender types. In single decision-maker environments, decision makers are better off ex ante if some of their uncertainty is resolved before they make a decision (Mossin 1969; Spence and Zeckhauser 1972). This, in turn, implies that expected payoffs are convex in the underlying probabilities. [5] Such convexities can then lead to certain kinds of increasing returns to information, as suggested by Radner and Stiglitz (1984).

   This convexity also generalizes to certain multi-decision-maker environments (see, e.g., Malueg and Xu 1993; Conlon 1999). In some signalling games, expected payoffs to the receiver are convex in the probability that the sender is honest, yielding a type of increasing returns to honesty (Conlon 1999). [6] It will be interesting to explore how general this sort of increasing returns to honesty result is.

   Section 2 presents a simple initial game without talk. Section 3 presents our central game and shows that sender honesty can yield negative and decreasing returns to the receiver. Section 4 shows that positive returns and convexity are restored if the receiver can precommit, and section 5 concludes.

2. A Simple Initial Signalling Game

   This and the next section present a signalling game with negative and decreasing returns to the receiver from sender honesty. This section presents a very simple signalling game--Game 1--and its equilibrium solution. The next section then extends the game to allow for talk. This extended Game 2 then illustrates negative and nonconvex returns to honesty. The solution to Game 2 is obtained by appropriate substitutions into the solution for Game 1.

   There are two players. Player I, the employee, has two possible types. He can be an employee with a small problem ([I.sub.SP]) or an employee with a big problem ([I.sub.BP]). The probability of his having a small problem is [alpha] and the probability of his having a big problem is 1 - [alpha]. Employees know their types.

   Player II is a mentor/supervisor. In her mentoring role, she wants employees to come to her for advice if they have problems. However, as a supervisor, if she believes that the employee has a big problem, she will want to investigate the situation to see whether the problem is the employee's fault. The employee does not want to be investigated, especially if the problem is, in fact, big. Thus, if the problem is big, he may not want to go to the supervisor for advice in the first place. Thus, the supervisor's desire to eliminate incompetent employees conflicts with her desire to help employees with problems.

   The supervisor cannot tell whether the employee has a small problem or a big problem. Thus, if an employee goes to her for advice, she must use Bayes' rule to determine the probability that the employee's problem is big or small.

   Thus, Player I either goes (G) to the supervisor or doesn't go (DG). Once Player I goes to the supervisor, the supervisor can either check up on the employee (C) or not check up on the employee (NC). In either case, the supervisor wants the employee to come to her so she can give him advice.

   We structure the payoffs as follows:

   (a) [I.sub.SP] will always prefer to go to the supervisor (even if the supervisor checks up on him, an employee with a small problem does not worry much about this since his problem is minor).

   (b) [I.sub.BP] will prefer to go to the supervisor if there is no risk of being checked up on and will prefer not to go if the investigation is certain.

   (c) II likes it when [I.sub.SP] or [I.sub.BP] goes to her, whether or not she checks up on them, since she wants to give the employee advice to help the employee solve the problem, whether big or small.

   (d) If II knows that she is facing a type of Player I who has a big problem, she will prefer to check up on him.

   (e) If II knows that she is facing a type of Player I who has a small problem, then she will prefer not to check up on him (e.g., it is not worth the effort).

   This game (Game 1) is represented in Figure 1, with Player I's payoffs given first. Thus, if I doesn't go (DG), he gets 3 and II gets 2, regardless of I's type. If [I.sub.SP] goes (G), he gets 4 [greater than] 3 or 5 [greater than] 3, depending on whether or not II checks up on him (C) or not (NC). Thus, [I.sub.SP] always prefers to go. Meanwhile, II gets 4 if she checks up on [I.sub.SP] and 5 if she does not. Thus, if she knows I is type [I.sub.SP], she will prefer not to check up on him. If [I.sub.BP] goes, he gets 0 [less than] 3 if checked up on and 5 [greater than] 3 if not. Thus, he will not go if he knows II will check up on him, but he will go if he knows II will not check up on him. Finally, II gets 4 if she checks up on [I.sub.BP] and 3 if she does not. Thus, if she knows that I is type [I.sub.BP], she will prefer to check up on him. [7]

   We use [[sigma].sub.I] and [[sigma].sub.II] to represent the behavioral strategies...