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ысшая школа экономики

International College of Economics and Finance

Graduate Work

Psychological Equilibria in Principal – Agent Theory:

Applications of Psychological Game Theory to Agency Theory.

Student (IV year, group 1):

Vadim Entin

Scientific adviser:

Doctor of economic sciences, PhD, associate professor

Alexei Belyanin

Moscow, 2010.

Contents
	Abstract ........................................................................................................................	2
1. Introduction..................................................................................................................		2
2.	Review of Relevant Literature .....................................................................................	5
3.	The model ..................................................................................................................	11
	3.1. The Set-up ...........................................................................................................	11
	3.2. The Game Form ..................................................................................................	14
	3.2.1. Game 1..........................................................................................................	14
	3.2.2. Stylized facts and possible equilibria. ..........................................................	17
	3.2.3. Advantages, Drawbacks and Possible Modifications...................................	21
	3.2.4. Model Summary and Further Investigation Possibilities .............................	24
4.	Conclusion .................................................................................................................	26
5.	References..................................................................................................................	27
Appendix........................................................................................................................		28

Abstract

Устанавливая в контрактах бонусные вознаграждения, зависящие от результатов работы агента, принципал, влияет не только на его внешнюю мотивацию (денежные стимулы,

возможности карьерного роста) но и на его внутреннюю мотивацию (личное восприятие трудового процесса и его результатов). Во множестве источников по агентской

(контрактной) теории, а также по теориям мотивации, подчеркивается важность внутренней мотивации и ее стимулирование. Соответственно, решения, предложенные в базовой интерпретации проблемы принципала-агента (см. источник [5]), не соответствуют объективной реальности, так как не учитывают внутренние компоненты мотивации. Цель данной работы – построить альтернативную модель контрактных отношений с поправкой на внутреннюю составляющую мотивации (объясненной в существующих теориях мотивации [6]), при помощи понятия психологических игр (см.

источник [2]), которая поспособствует устранению разногласий между экономическими и психологическими подходами к агентской теории.

1. Introduction

The principal-agent theory is a vast field of study, concerning the relationships of two parties with often opposing interest, namely, an agent and a principal. Remarkably, this problem has been an issue in different fields of social science: in economics and political science, known as agency theory, in sociology and psychology known as the

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conflict of interests. The developments in P-A theory lead the economic perspective to consider motivation more thoroughly and place an emphasis on its role in the solutions to the P-A problem.

The aim of this work is to analyze one particularly interesting issue of agency theory – the problem of moral hazard in labor relationships (also known as contract theory) from a perspective that would enable us to reconcile the often opposing views of economists, sociologist and psychologists on the issue and find possible solutions to the problem. The instruments, that would be helpful in building a bridge between the two opposing viewpoints, were developed in the many works of economic and sociological as well as psychological scientists, on this issue. In later works there has been a positive trend in economic works to aim at receiving psychologically and sociologically adequate solutions to the problem. For instance, the development and wide discussion of the importance of intrinsic motivation, and how it is opposed to the extrinsic motivation (monetary rewards, career achievements) has been discussed in numerous articles on P- A theory and motivation.

The analytical tool that in this work is considered to have a potential for the solution of the P-A conflict is drawn from the work on the so named psychological game theory, which introduces a psychological component to the well-known and applied game theory. A psychological game differs from an ordinary game, in the way its payoffs are determined. In a psychological game the payoffs of the agents depend not only on the strategies chosen, but also on one‟s beliefs about the strategy choice of the counterparty.

In synthesis the basic model of moral hazard in contract theory with addition of intrinsic motivation component and the psychological game yield quite a compact but an informative model, with some interesting implications. Prior to the model set up, part 2 of this diploma will provide a thorough review of the most influencing works

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concerning the subject matter as well as a brief review of relevant works in the related subjects (agency theory, motivation and psychological games). Part 3 will be devoted entirely to the model description and its implications, as well as possible developments and advice on how this model can be further investigated and tested. Finally, Part 4 will conclude and summarize the achieved results.

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2. Review of Relevant Literature

This work uses two major works in agency theory and psychological game theory, respectively, as a base for modeling, as well as numerous sources on motivation, to adjust for this important component in the model developed below. After searching for the relevant literature, numerous works on agency theory were found, and a pronounced trend to the growing interest to intrinsic motivation from the economists is observed. Numerous articles were found, studying the behavioral aspects of motivation. In this part particular attention will be devoted to a remarkable work on extrinsic and intrinsic motivation by Bénabou and Tirole [1], in order to depict the ideas that inspired the theoretical model in Part 3. Following, the author will provide an overview of the article devoted to psychological game theory [2], as it is the main instrument of analysis of the model provided below, also allowing to adjust the model for psychological aspects, and provide a somewhat alternative approach to P-A theory, preserving its implications, concerning both optimality and motivation. Afterwards, the sources that provide a good framework for the analysis of contract theory, and sources that enable modeling of intrinsic motivation within an economic model are discussed in some detail. Finally, other related articles will be briefly reviewed.

In their work, Bénabou and Tirole [1] discuss the different psychological stimuli that may affect the intrinsic motivation of an agent, and different incentives strategies - from performance or result contingent rewards to delegation, coaching and help; as well as their influence on intrinsic motivation. They discuss the issue of „forbidden fruit‟ and the „Tom Sawyer Effect‟ as we may call it.

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The authors start their analysis with the economic framework of “The Looking-Glass

Self”, after Cooley1, which they further use to approach the P-A problem. They then proceed to address the problem of hidden costs of rewards, which is a particularly interesting issue. The authors assume that prior to accepting the work on some project, the agent does not poses full information on how hard the execution of task, i.e. the disutility of effort, while the principal, who has previously faced similar projects, has a clear view on how hard the work is. Alternatively, if the agent knew hard the task is, any bonus for him would be a positive stimulus to exert high effort, however, as long as the agent is unaware of its magnitude, the size of bonus serves as a signal on the complexity of the task, and along with a stimulating effect in the short run, has a negative long-run effect on the worker‟s intrinsic motivation: once the bonus is offered, the agent perceives the signal and internalizes the principal‟s view of the work complexity, so that next time he is considering a similar project, he already has a belief on the disutility of effort, and expects a particular bonus. From this perspective it is arguable if indeed contingent rewards are positive reinforces, or, as the psychologists claim – a negative one.

The authors further address alternative incentive schemes, such as “burning money”, whereby principals increase the base payment decreasing the contingent part. In so doing they signal the confidence they have in their agents, thus positively affecting the agent‟s intrinsic motivation. This finding underlines the importance of trust and reciprocity in P-A relationships. The latter is an issue of numerous articles, some of which are discussed below. In the remainder of the article the authors deal with confidence management techniques and costs and benefits of ego bashing and ego

1 Cooley, C. (1902), Human Nature and the Social Order, Charley Scribner‟s Sons.

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boosting2. The notion of intrinsic motivation discussed in this article, though from a different perspective, is central in the model discussed in Part 3.

The theoretical tool that can enhance the analysis of agency theory from a more psychological perspective is provided by Geanakoplos, Pearce and Stacchetti in their work on psychological game theory [2]. They thoroughly developed the idea of psychological games, the game theory where the players‟ payoffs depend on their multilevel beliefs about other player‟s strategies and the beliefs about other player‟s beliefs. Along with formal mathematical definitions of players‟ strategy sets and belief hierarchies, which might seem somewhat puzzling, the article presents sufficient and accessible visual representation of psychological games in the normal form, or as the authors call it the “summary form”3. Defining the properties of belief hierarchies and their topology (for details see source [2]) the authors start with considering the games in the normal form, where they stress the important feature of psychological equilibria, namely the fact that they cannot be found through backward induction, as opposed to ordinary games. They, however, devote a significant attention to the formal proof of existence of psychological Nash equilibrium or multiple equilibria in psychological games, as well as the more peculiar to psychological games trembling hand perfect equilibria, discussed in much detail in the part on extensive form psychological games. For the sake of the model developed in Part 3 of this work, the predominant tool will be the notion of the summary form game.

2For details see the article [1]

3The summary form limits the belief hierarchy to a smaller dimension, to simplify the model without loss of generality (for example in reality, the players payoff might depend not only on beliefs about other player‟s strategy, but also on the other player‟s beliefs about one‟s beliefs about other player‟s strategies, etc.; however, the authors claim that limiting the levels of beliefs up to the second order beliefs, will significantly simplify the analysis without seriously affecting the accuracy of results).

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Though part of the article‟s notions and mathematical instruments and definitions along with proofs are beyond the scope of this work, their notion of normal form psychological games and the so-called summary form of the game may prove to be very handy and useful in approaching the P-A theory.

The framework, within which the model is developed, is drawn from the textbooks in industrial economics [3] and organization theory [4]. While the former provides a formal and very detailed description of contract theory from an economic perspective, the latter, explains graphically many peculiarities of agency theory, as well as noting many important assumptions, when approaching the issue. A very accessible setup of the model can be found in the LSE subject guide in industrial economics [5], and the model in Part 3, widely uses this setup and notions.

The managerial (sociological) perspective of incentives is presented in detail in yet another textbook on organizational theory. A very minute description of drives and motives and different motivation theories can be found in chapter on motivation in Huczynski and Buchanan [6]. Multiple content and process theories of motivation, are depicted in this chapter including the well-known Maslow needs hierarchy, the equity theory, which states, that drives for any action are rooted in situations of inequity, and aimed at reestablishing equity, and the expectancy theory, that describes the process whereby the outcomes become desirable. The latter theory was used in development of the model in Part 3: Vroom4 explains that the motivational „force‟ for action is the product of valence, instrumentality and expectancy, summed for all possible outcomes:

F V I E . E, the expectancy variable is said to be fixed for all outcomes, as it denotes „the probability that high effort will lead to high performance‟. From this definition of E we may draw a parallel to the probability variable x used in the P-A

4 Vroom, V.H. (1964) Work and Motivation, New York: Wiley, 331

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model outlined by Symeonidis [5]. The very interesting implication of Vroom‟s theory is that for the „force‟ to be positive all three components of it should be non-zero. This implication is referred to, when modeling the intrinsic motivation function as a product of beliefs and valence in Part3.

The sources above provided all the required resources for the framework outlined in Part 3. The author has searched the databases for articles, that attempted to describe a similar model, however, the most similarity with this work remains with the work of

Bénabou and Tirole [1] and the published graduate qualification work of one of the graduates of 2005 [9]. Below the author will briefly mention articles that are related to the issue in some perspective.

Bénabou and Tirole [1] refer in their article to the works of Deci and Ryan, who present a thorough psychological view on motivation in their book [7], and some experimental empirical evidence [8]. Their findings led to identification of three psychological needs that demand satisfaction in order to yield high internal motivation, namely competence, autonomy and relatedness. Accounting for these needs is also observable in the model in part 3, however, is implicit, as it is assumed to be summarized in actors‟ beliefs.

In further investigation, of cross-references other articles on related subjects were discovered. For instance, J. Sobel (2005) [10] provides an insight to non-selfish behavior, and reciprocity. Tirole [11] has addressed the economics of self-management identifying existence of motivated beliefs, and stressing the importance of will-power and self-confidence in work. Sliwka [12] has further investigated hidden costs of incentive schemes from the perspective of signaling.

Frey and Jegen [13] present a survey of empirical evidence on motivation crowding, and is a sizeable source of references on the subject, which is why the reader is advised to refer to this work in order to get an insight if the issue, and find more related articles

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