Optimal Contracting Under Adverse Selection: The Implications of Mentalizing

We study a model of adverse selection, hard and soft information, and mentalizing ability — the human capacity to represent others’ intentions, knowledge, and beliefs. By allowing for a continuous range of different information types, as well as for different means of acquiring information, we develop a model that captures how principals differentially obtain information on agents. We show that principals that combine conventional data collection techniques with mentalizing benefit from a synergistic effect that impacts both the amount of information that is accessed and the overall cost of that information. This strategy affects the properties of the optimal contract, which grows closer to the first best. This research provides insights into the implications of mentalizing for agency theory.


Introduction
Agency theory posits that informational asymmetry, whether modeled as an instance of hidden action or hidden knowledge, hinders the contracting parties from obtaining the first-best outcome (Holmström, 1979;Laffont & Martimort, 2002;Ross, 1973). The theory also allows individuals to partly reduce informational barriers by (in the case of the agent) signaling or (in the case of the principal) learning the agent's type and monitoring his effort. These activities, however, are treated in a highly stylized manner. For instance, in the standard moral hazard model, all signals on the agent's effort can be included in the contract between the principal and the agent and are assumed to be verifiable. In fact, many signals on agents' efforts are verifiable but some are not, and principals may rely on non-verifiable information (e.g., body language and facial expressions) to assess an agent's effort. Similarly, in the adverse selection model, principals may rely on such soft psychological information in assessing agents' types.
In other words, information is an essential component of agency theory, and yet it is often modeled in a way that abstracts from some potentially key features of the real world. This paper addresses exactly this problem. Specifically, information differs substantially depending on its form, and recent research has begun to capture this fact by classifying it in terms of how hard versus soft it is (Godbillon-Camus & Godlewski, Issue 2 2015215-232 2006Peterson, 2004). Hard information (e.g., a person's education level, experience, or income) is easily reduced to numbers, it can be collected in an impersonal way, and its meaning is less contingent on subjective judgements, opinions, or perceptions. On the other hand, soft information (e.g., a person's feelings, perceptions, values, or motivations) is difficult to accurately reduce to a numeric score, and its meaning is highly dependent on the context in which it is collected and on the personal opinions and perceptions of the person collecting it.
If information differs in terms of how hard or soft it is, it is pertinent to ask whether there are ways of obtaining it that are particularly suitable, depending on the type of information. Recent convergent developments in evolutionary anthropology (Call & Tomasello, 2008), cognitive neuroscience (Gallagher & Frith, 2003), and neuroeconomics (Singer & Fehr, 2005) highlight the importance of players' mentalizing-that is, their intersubjective understanding of preferences, intentions, knowledge, and beliefs. Information about these mental states is soft in nature and is crucially important in making sense of and predicting the behaviors of others (Singer & Fehr, 2005). Thus, mentalizing is ideally suited for the acquisition of soft information.
There is no reason to suppose that principals should not make use of mentalizing as a preferred method of inferring information about other players.
As Singer and Fehr (Singer & Fehr, 2005) note, however, economists take a technical shortcut by assuming a common prior distribution over agent types without considering the determinants of this distribution. In other words, agency theory does not make explicit room for mentalizing. Yet, the theory effectively if implicitly assumes that the principal has perfect access to and knowledge of certain mental states of the agent (Foss & Stea, 2014). For example, in the standard moral hazard model (Holmström, 1979), the principal is assumed to know the risk preferences and reservation utility of the agent.
The object of this paper is to provide insights into the implications of mentalizing for agency theory. We base our analysis on a manager-worker relationship under adverse selection (Laffont & Martimort, 2002) where we allow for a continuous range of different information types and different means of acquiring in-formation. We obtain three main sets of results. First, we show that mentalizing can be a low-cost method of acquiring information. Second, we show that mentalizing provides access to information that may be difficult to elicit in other ways. Third, we highlight that mentalizing impacts the design of the bilateral contract that the principal and agent sign, resulting in an increase in the volume of trade achieved under asymmetric information. All in all, this research suggests that a more nuanced description of how principals differentially obtain information on agents leads to a more accurate modeling of agency relationships.

The basic model with an informative signal
The basic adverse selection model with an informative signal (Laffont and Martimort, 2002) includes a principal P and an agent A . The principal wants to delegate to the agent the production of q units of a good. The value for the principal of these q units is Moreover, for a menu to be accepted, the following two participation constraints must be satisfied: The principal's problem consists of finding the solu- is the second-best contract offered in the absence of an informative signal.

The principal's expected utility
Thus far we have followed (Laffont & Martimort, 2002). We now want to change our viewpoint slightly and formulate the optimization problem in terms of the principal's overall expected utility.
This provides a way for us to merge the optimi- where the contracts are subject to (2.3)-(2.6). Writing the right-hand side of (2.10) in the form

More information is better
Intuitively, we expect it to be advantageous for the principal to have access to additional information about the agent. In this section, we prove that this is indeed the case within the framework of the basic model of Section 2.
For simplicity, we henceforth suppose that 1 2 = = µ µ µ, where µ is the informativeness of the signal. Then, in view of (2.8), The expected utility in the absence of an informative signal is obtained by setting = 1/ 2 µ : Optimal Contracting under Adverse Selection: The Implications of Mentalizing The following theorem expresses the fact that it is always beneficial for the principal to take additional information into account when formulating the contract.
The more informative the signal σ is, the higher is the principal's expected utility.

Theorem 3.1 The principal's expected utility function E ( )
V µ is strictly convex and attains its minimum at The calculation shows that the last two terms on the right-hand side of (3.3) cancel. Thus, Differentiating once more, we find S q q and the parameter values given in (3.4).
Remark 3.2 The conclusion of Theorem 3.1 is reminiscent of the conclusion of Holmström's sufficiency theorem (Holmström, 1979). The contexts of these theorems differ in that the timing and setup of the contracting process are different.

Example 3.3
Consider the special case of ( ) = 2 S q q . In this case, . In Figure 1 the graph of E ( ) V µ is shown for the following choices of the parameters:

The basic model with a costly informative signal
We saw in the preceding section that the principal always benefits from additional information when formulating the contract. Thus, if information is free, the principal will always choose to acquire maximal information. In a more realistic scenario, there is a cost associated with the information in the signal σ (for example, the effort cost of the principal to obtain that information). In this section, we analyze the consequences of the information signal being costly.
Consider the model of Section 3 with an information signal of informativeness µ , where µ ranges from 1/ 2 (no additional information) to 1 (full information), but suppose now that the information in the signal σ is costly for the principal. More precisely, suppose the principal's utility has the form where ( ) C µ is the cost of obtaining a signal of informativeness µ . The principal's problem consists of solving the optimization problem (cf. (2.10)) For fixed µ , the solution is given by (  Issue 2 2015 215-232 , where ( ) f µ is given by (3.2).
Example 4.1 Consider the information cost function where > 0 c is a constant, see Figure 2. Because information. Clearly, the extent to which a given piece of information can be hard or soft differs and the above distinction is to be seen as a continuum along which information can be classified (Petersen, 2004).
Given this, we now assume that there is a continuous range of different types of information. The in-formation types are labeled by the variable the relation (5.1) implies that µ ranges from 1/ 2 to 1. We will denote by ( , ) C x y the cost for the principal of obtaining an amount In view of (2.7), the problem reduces to maximizing the principal's expected utility For these parameter values, the principal's expected

Different ways of obtaining information
The ability to put oneself in another person's shoes has long been recognized as a crucial aspect of social interaction (Aumann & Brandenburger, 1995;Fudenberg & Tirole, 1991;Schutz, 1932;Weber, 1979). In particular, this ability serves as a key mechanism for coordinating beliefs and actions. Recent research in evolutionary anthropology (Call & Tomasello, 2008), cognitive neuroscience (Gallagher & Frith, 2003), and neuroeconomics (Singer & Fehr, 2005) highlights the importance of an individual's mentalizing processes-that is, her understanding of another individual's intentions, knowledge, and beliefs (Singer & Fehr, 2005). These are mental states that are not directly observable but are useful because they can make sense of, and predict, the behaviors of others (Call & Tomasello, 2008;Premack & Woodruff, 1978;Singer & Fehr, 2005).
First, the ability to understand intentions-that is, plans of action chosen in pursuit of a goal (Bratman, 1989;Dennet, 1987)-represents the first interpretive matrix for deciding what someone is doing (Tomasello et al., 2005). For example, suppose that an agent is working several extra hours and that a principal wants that agent to maintain his effort. The action of working extra hours, however, may have extremely different intentional connotations. The agent may be intrinsically motivated to deliver a good performance, or he may be externally motivated to do so by the potential for a monetary bonus. While giving a monetary reward to the extrinsically motivated agent could be a proper way to incentivize him, giving the same reward to an intrinsically motivated agent may crowd out the intrinsic motivation and even diminish the overall effort (Frey & Jegen, 2001). Second, an agent's intentions are highly influenced by his knowledge. For this reason, the contextualization of an individual's intentions relative to an understanding of her knowledge is another fundamental constituent of mentalizing. In terms of the above example, if the principal knows that the agent knows that the organization has recently implemented a new reward system, the principal may expect the agent to work harder to obtain a bonus (rather than because of an innate interest in the task). Finally, as beliefs are by definition mental, the ability to understand someone's beliefs has been defined as the most complex component of mentalizing (Tomasello et al., 2005). In terms of the example, suppose that the principal knows that the agent works extra hours because of the reward system. Suppose the principal also knows that the agent is ignorant of the output-based (as opposed to input-based) nature of the reward criterion-in other words, the principal knows that the agent is wrong in thinking that his extra work will automatically result in higher compensation. The principal may benefit from this more nuanced understanding, and decide to not inform the agent about his mistaken belief.
Neuroscience research shows that humans have a brain system that is dedicated to mentalizing and that specific brain regions are activated when people engage in automatic as well as deliberate mentalizing Gallagher & Frith, 2003). Further, mentalizing may be understood as a skilled behavior in that it is program-like (i.e., mentalizing consists of an ordered sequence of cognitive steps), it is built upon a mixture of tacit and explicit knowledge (in fact, rarely is the mentalizer completely aware of the mechanisms that engender his having a theory of the other's mind), and it requires the making of a certain number of choices that vary in terms of the degree of intentionality (i.e., automatic versus deliberate mentalizing).
Information about an individual's intentions, knowledge, and beliefs is better captured in text than in a numeric score. Further, it must be collected in person and its meaning is likely to be highly contingent  Godlewski, 2006;Petersen, 2004). Therefore, mentalizing is ideally suited for the acquisition of soft information. On the other hand, given its subtle psychological nature, mentalizing is not well suited for the acquisition of hard information, as this type of information is better captured by more conventional (hard) data collection techniques. The opposite applies to these other techniques, which are ideally suited for the acquisition of hard types of information, but not for that of soft information.
As an example, consider the following two pieces of information regarding a hypothetical software engineer (agent). First, the agent holds a master's degree and has some years of work experience. Second, the agent loves the technical nature of his work and is entirely driven by this passion in his daily activities.
A principal that would want to obtain the first bit of information (education and experience) would find it much easier to do so by simply looking at the hard data on the employee's curriculum vitae. Clearly, he would find it extremely difficult to reach the same conclusions by exclusively mentalizing with the agent.
On the other hand, there hardly is any way for a curriculum vitae to capture in an accurate and reliable way an agent's innate passions and interests. Thus, a principal that wants to obtain this information would be better served by trying to put herself in the agent's shoes-e.g., by looking at how the agent talks about his work-related activities-so as to have a feeling of what drives that agent in his function as software engineer.
In other words, it is easier to obtain soft information via mentalizing than via hard data collection. Similarly, it is easier to obtain hard information via hard data collection than via mentalizing.
As in the preceding section, we assume that there exists a continuous range of different types of information labeled by the variable corresponds to hard information and = 1 x corresponds to soft information. In line with the above argumentation, we now also assume that the principal has two different ways of obtaining information: he can either use data collection or mentalizing. We will denote by Lastly, the principal's expected utility when acquiring information as dictated by

Comparisons
If the principal were to obtain the information described by the function ( ) max I x in (6.5) using only data collection (and did not have access to mentalizing), then the expected utility would decrease from  In summary, by combining both data collection and mentalizing, the principal takes advantage of a synergistic effect which impacts both the amount of information that can be accessed and the overall cost of accessing that information. Mentalizing provides access to information that would not be possible to elicit using data collection only, and data collection provides access to information that would not be possible to elicit by using mentalizing only. Additionally, the average cost for any given amount of information is lower when the principal can selectively decide to use mentalizing or data collection depending on the nature of the information itself. This is reflected in the principal's expected utility, which is higher when he can make use of both data collection and mentalizing.

Implications
What are the implications of mentalizing for the contracting process? We now explore how transfer and production levels, as well as the principal's expected  The expected transfers and production levels as functions of the mentalizing ability m (solid) and the corresponding first-best values (dotted). In the case of E ( ) SB q m , the solid and dotted lines coincide because the efficient agent's production level is the same for the first-best and second-best solutions, see equation (2.9).

Summary and conclusions
Recent developments in evolutionary anthropology (Call & Tomasello, 2008), cognitive neuroscience (Gallagher & Frith, 2003), and neuroeconomics (Singer & Fehr, 2005) highlight the importance of players' intersubjective understanding of preferences, intentions, and beliefs. When a player makes inferences about such mental states, she mentalizes-that is, she forms conjectures about mental states that are not directly observable but are useful because they can make sense of and predict the behaviors of others (Singer & Fehr, 2005).
The purpose of the present paper has been to define a space for mentalizing in principal-agent theory. We have taken some initial steps towards a more nuanced description of how principals differentially obtain information on agents by considering an extension of the basic adverse selection model, allowing for a continuous range of different information types as well as for different means of acquiring information. Our point of departure has been that principals are likely to resort to both conventional data collection tools as well as mentalizing processes when extracting information about an agent. Given its subtle psychological nature, mentalizing is ideally suited for the processing of soft information. On the other hand, hard information is better captured by more conventional approaches.
Within the context of our model, we have observed that by combining both data collection and mentalizing, the principal can take advantage of a synergistic effect that impacts both the amount of information that can be accessed and the overall cost of accessing that information. This observation is reflected in the transfer and production levels as well as in the principal's utility. A high ability to mentalize drives these quantities closer to the first-best values that would be obtained in a scenario with perfect information. All in all, this research shows that a diversified approach to information acquisition leads to a refined preparation of the menu of contracts and a more efficient delegation.