EUROPEAN BUSINESS SCHOOL
International University Schloß Reichartshausen
Seminar Paper
Finance and Banking
Seminar International Corporate Finance
Winter Term 2003

Applying Game Theory in Finance

by

 Christian Funke

Table of Contents

List of Abbreviations  II

1 Introduction  1
1.1 Problem and Objective of the Paper  1
1.2 Organization of the Paper  1

2 Game Theoretic Foundations  2
2.1 Basic Definitions  2
2.2 Nash Equilibrium, Dominance, and Rollback  4
2.3 Asymmetric Information  6

3 Game Theory in the Context of Finance  7
3.1 First Game Theoretic Concepts in Finance  7
3.2 Enhancing Financial Theory with Game Theoretic Modeling  8

4 Selected Applications of Game Theory in Finance   9
4.1 Dividends as Signals of Future Cash Flows  9
4.2 Signaling and Agency Models of Capital Structure Decisions  12
4.3 Other Areas of Game Theory Application in Finance  14

5 Critique & Concluding Remarks  15

Appendix  17

References  20

List of Abbreviations
eds. editors
ed. edition
IPO Initial Public Offering
MM MODIGLIANI & MILLER
NPV Net Present Value
no. number
vol. volume

1 Introduction

1.1 Problem and Objective of the Paper

The groundbreaking work of MODIGLIANI & MILLER (MM)¹ introduced the rigors of economic analysis to financial research. This is “generally cons idered the beginning point of modern managerial finance.”² Their first economic models were challenged by financial practitioners for being overly simplistic in their assumptions and therefore lacking real world application value.³ MM acknowledged and addressed this fact in their first paper.⁴ Later models relaxed some assumptions, such as symmetric information or complete contracts, while trying to retain an explanatory value in the spirit of the original MM papers.⁵

This incorporation of more realistic elements, such as strategic interaction and asymmetric information, brought several problems to financial economists’ models: they required a lot of definitions, became even more complex, and were not easily comparable. Game theory provided a solution for those problems in its first applications to economics in the 70s and 80s: a set of common definitions and a basic language to guarantee comparability and empirical testability of financial models using game theoretic concepts. ⁶ Nowadays, there are few issues in finance research which have not been modeled by applying game theoretic concepts⁷, and therefore it is crucial to be familiar with the basics of game theory and its application in finance.

The objective of this paper is to provide an intuitive approach to game theory in finance by first giving an overview of the basic foundations of game theory, and then providing a survey of some selected applications most relevant to the financial practitioner.

1.2 Organization of the Paper

The paper first develops the necessary foundations in chapter 2 to introduce the specific language and the most important theoretical concepts of game theory, and to demonstrate their application value in real world problems. The chapter serves to define game theory in the scope of this paper and explores the basic concepts needed to solve games of strategy. Special consideration is given to the incorporation of asymmetric information, as this area of research in game theory is most important to financial applications. Hence, it is central to the discussion in the following chapters.

This is shown in chapter 3, which explores how ideas of asymmetric information can be applied in finance. It aims to provide an intuitive approach to the subject by discussing early models of asymmetric information in finance. Building on those models, it demonstrates the usefulness of game theoretic concepts to enhance the economic modeling.

A survey of game theory in finance in chapter 4 integrates the prior chapters by showing the real application value of game theory with important historic and current examples. It provides a discussion of published papers using game theoretic concepts to enhance the understanding of two unresolved issues in finance: dividend and capital structure policy. To give a complete overview of game theoretic models in finance, it also provides selected examples from other areas, such as the market for corporate control, Initial Public Offerings (IPOs) and financial intermediation. However, taking the overall seminar topic into account this paper will mainly focus on corporate finance.

Finally, chapter 5 serves the purpose of closing the discussion with some critical remarks and drawing conclusions. Some current areas of research are addressed in order to indicate recent advances in game theory and the application possibilities in finance.

2 Game Theoretic Foundations

“Game theory comprises formal mathematical models of ‘games’ that are examined deductively.” ⁸ These models provide three advantages: (1) a clear and precise language to transfer insights from one context to another, (2) the possibility to cross-check those insights for logical consistency, and (3) the ability to trace back conclusions directly to the assumptions.⁹ This chapter provides an introduction to the most important concepts of game theory and lays the ground for its applications in the context of finance.¹⁰

2.1 Basic Definitions

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1 The MM capital structure irrelevancy propositions were published in MODIGLIANI/MILLER (1958) and MODIGLIANI/MILLER (1963), the dividend irrelevancy propositions in MODIGLIANI/MILLER (1961). For a discussion of the MM propositions ‘40 years later’ see MILLER (1998).

2 ROSS/WERSTERFIELD/JAFFE (2002), p. 397.

3 See ALLEN/MORRIS (2001), p. 23; MM assume perfect and complete markets.

4 See MODIGLIANI/MILLER (1958) pp. 272-276 and p. 296.

5 See e.g. ALLEN/MICHAELY (1995), pp. 802-832 for a good survey of the literature on dividend policy.

6 See ALLEN/MORRIS (2001), p. 23; DIXIT/SKEATH (1999), p. XIX; KREPS (1990) pp. 5-7.

7 See ALLEN/MORRIS (2001); THAKOR (1991); THAKOR (1989) for surveys.

8 KREPS (1990), p. 6.

9 See KREPS (1990), p. 6-7.

10 For a thorough introduction to game theory see DIXIT /SKEATH (1999); KREPS (1990); FUDENBERG/TIROLE (1991). The first substantial text of game theory is NEUMANN/MORGENSTERN (1947).