Investment under Uncertainty. Coalition Spillovers and Market Evolution in a Game Theoretic Perspective

1. Auflage 2004
ISBN: 978-1-4020-7944-3
Verlag: Kluwer Academic Publishers
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 255 Seiten

Two crucial aspects of economic reality are uncertainty and dynamics. In this book, new models and techniques are developed to analyse economic dynamics in an uncertain environment. In the first part, investment decisions of firms are analysed in a framework where imperfect information regarding the investment's profitability is obtained randomly over time.

In the second part, a new class of cooperative games, spillover games, is developed and applied to a particular investment problem under uncertainty: mergers. In the third part, the effect of bounded rationality on market evolution is analysed for oligopolistic competition and incomplete financial markets.

Written for: Researchers, scientists

The Author

Dr. Jacco J.J. Thijssen graduated in Econometrics from Tilburg University, Tilburg, The Netherlands in 1999. In the same year he also completed the Master’s Program in Economics from CentER at the same university. After that, he carried out his Ph.D. research at the Department of Econometrics & Operations Research, and CentER at Tilburg University. Since September 2003 he is a.liated as a Lecturer in Economics with the Department of Economics at Trinity College Dublin, Dublin, Ireland.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Contents;6
2;List of Figures;10
3;Acknowledgments;12
4;Chapter 1 INTRODUCTION;13
4.1;1. Rational Behaviour and Economics;13
4.2;2. Introduction to Part I;17
4.3;3. Introduction to Part II;22
4.4;4. Introduction to Part III;25
5;Chapter 2 MATHEMATICAL PRELIMINARIES;32
5.1;1. Basic Concepts from Topology and Calculus;32
5.2;2. Convex Analysis;35
5.3;3. Triangulations;36
5.4;4. Game Theory;37
5.4.1;4.1 Non-Cooperative Theory;38
5.4.2;4.2 Cooperative Theory;40
5.5;5. Basic Concepts from Probability Theory;43
5.6;6. Markov Chains;46
5.6.1;6.1 Stochastic Stability;47
5.6.2;6.2 Nearly-Complete Decomposability;50
5.7;7. Stochastic Processes in Continuous Time;54
5.7.1;7.1 Basic Stochastic Processes;59
5.7.2;7.2 Optimal Stopping;61
6;Chapter 3 THE EFFECT OF INFORMATION STREAMS ON CAPITAL BUDGETING DECISIONS;64
6.1;1. Introduction;64
6.2;2. The Model;67
6.3;3. The Optimal Investment Decision;69
6.4;4. Error Analysis;74
6.5;5. Economic Interpretation;75
6.6;6. Conclusions;81
6.7;Appendix;82
6.7.1;A. Proof of Proposition 3.1;82
6.7.2;B. Proof of Proposition 3.2;83
7;Chapter 4 SYMMETRIC EQUILIBRIA IN GAME THEORETIC REAL OPTION MODELS;86
7.1;1. Introduction;86
7.2;2. The General Model;89
7.2.1;2.1 The Equilibrium Concept;90
7.2.2;2.2 Preemption Games;97
7.3;3. The Standard Model;99
7.4;4. The Interaction of Competition and Uncertainty;101
7.4.1;4.1 Equilibrium Selection;104
7.4.2;4.2 The Impact of Uncertainty on Equilibria;107
7.4.3;4.3 The E.ect of Competition on the Value of Waiting;108
7.4.4;4.4 The E.ect of Uncertainty on Welfare Predictions;109
7.5;5. Conclusion;112
7.6;Appendix;113
7.6.1;A. Proof of Theorem 4.1;113
7.6.2;B. Some Integrals;117
8;Chapter 5 THE EFFECTS OF INFORMATION ON STRATEGIC INVESTMENT;119
8.1;1. Introduction;119
8.2;2. The Model;123
8.3;3. Exogenous Firm Roles;127
8.4;4. Endogenous Firm Roles;128
8.4.1;4.1 Dominant First Mover Advantage;129
8.4.2;4.2 Dominant Second Mover Advantage;131
8.5;5. Welfare Analysis;135
8.6;6. Conclusions;140
8.7;Appendix;141
8.7.1;A. Proof of Proposition 5.1;141
8.7.2;B. Proof of Lemma 5.1;143
8.7.3;C. Proof of Proposition 5.2;144
8.7.4;D. Proof of Proposition 5.3;145
9;Chapter 6 SPILLOVERS AND STRATEGIC COOPERATIVE BEHAVIOUR;149
9.1;1. Introduction;149
9.2;2. The Model;151
9.3;3. The Core;154
9.4;4. Public-Private Connection Problems;156
9.5;5. Government Situations;160
9.5.1;5.1 The Power Index;161
9.6;6. Mergers in Oligopolistic Markets;163
9.6.1;6.1 The Compromise Value;165
9.7;Appendix;169
9.7.1;A. Proof of Theorem 6.1;169
9.7.2;B. Constructing a Spillover Game from a Non- Cooperative Game;170
10;Chapter 7 THE TIMING OF VERTICAL MERGERS UNDER UNCERTAINTY;171
10.1;1. Introduction;171
10.2;2. The Model;173
10.3;3. The Effect of the Stand-Alone Option on the Timing of Mergers;176
10.4;4. Implications;180
10.5;Appendix;181
10.5.1;A. Proof of Proposition 7.1;181
11;Chapter 8 MULTI-LEVEL EVOLUTION IN COURNOT OLIGOPOLY;184
11.1;1. Introduction;184
11.2;2. The Model;187
11.2.1;2.1 The Quantity Setting Level;188
11.2.2;2.2 The Behavioural Level;189
11.3;3. Analysis;192
11.4;4. Conclusion;198
11.5;Appendix;199
11.5.1;A. Proof of Lemma 8.1;199
11.5.2;B. Proof of Lemma 8.2;200
12;Chapter 9 EVOLUTION OF CONJECTURES IN COURNOT OLIGOPOLY;201
12.1;1. Introduction;201
12.2;2. The Model;205
12.3;3. A Simulation Study;208
12.4;4. A Theoretical Analysis;211
12.5;5. Discussion;218
12.6;Appendix;219
12.6.1;A. Proof of Lemma 9.1;219
12.6.2;B. Proof of Lemma 9.2;220
13;Chapter 10 BOUNDED RATIONALITY IN A FINANCE ECONOMY WITH INCOMPLETE MARKETS;221
13.1;1. Introduction;221
13.2;2. The Finance Economy;224
13.3;3. Existence of Equilibrium;226
13.4;4. A Boundedly Rational Path Towards Equilibrium;232
13.5;5. The Algorithm;235
13.6;References;241
14;Author Index;251
15;Subject Index;253
16;About the Author;255
17;More eBooks at www.ciando.com;0

Leseproben

Chapter 4 SYMMETRIC EQUILIBRIA IN GAME THEORETIC REAL OPTION MODELS (p. 77-78)

1. Introduction

The timing of an investment project is an important problem in capital budgeting. Many decision criteria have been proposed in the literature, the net present value (NPV) rule being the most famous one. In the past twenty years the real options literature emerged (cf. Dixit and Pindyck (1996)) in which uncertainty about the pro.tability of an investment project is explicitly taken into account. In the standard real option model the value of the investment project is assumed to follow a geometric Brownian motion. By solving the resulting optimal stopping problem one can show that it is optimal for the .rm to wait longer with investing than when the firm uses the NPV approach.

A natural extension of the one firm real option model is to consider a situation where several firms have the option to invest in the same project. Important fields of application of the game theoretic real options approach are R&D competition, technology adoption and new market models. Restricting ourselves to a duopoly framework, the aim of this chapter is to propose a method that solves the coordination problems which arise if there is a .rst mover advantage that creates a preemptive threat and, hence, erodes the option value. In the resulting preemption equilibrium, situations can occur where it is optimal for one firm to invest, but not for both. The coordination problem then is to determine which firm will invest. This problem is particularly of interest if both firms are ex ante identical. In the literature, several contributions (see Grenadier (2000) for an overview) solve this coordination problem by making explicit assumptions which are often unsatisfactory. In this chapter, we propose a method, based on Fudenberg and Tirole (1985), to solve the coordination problem endogenously.

The basic idea of the method is that one splits the game into a timing game where the preemption moment is determined and a game that is played either as soon as the preemption moment has been reached, or when the starting point is such that it is immediately optimal for one firm to invest but not for both. The outcome of the latter game determines which firm is the .rst investor. The .rst game is a game in continuous time where strategies are given by a cumulative distribution function. The second game is analogous to a repeated game in which firms play a fixed (mixed) strategy (invest or wait) until at least one firm invests.

As an illustration a simplified version of the model of Smets (1991) that is presented in Dixit and Pindyck (1996, Section 9.3), is analysed.

In the preemption equilibrium situations occur where it is optimal for one firm to invest, but at the same time investment is not beneficial if both firms decide to do so. Nevertheless, contrary to e.g. Smets (1991) and Dixit and Pindyck (1996), we .nd that there are scenarios in which both firms invest at the same time, which leads to a low payo. for both of them. We obtain that such a coordination failure can occur with positive probability at points in time where the payoff of the first investor, the leader, is strictly larger than the payo. of the other firm, the follower. From our analysis it can thus be concluded that Smets’ statement that "if both players move simultaneously, each of them becomes leader with probability one half and follower with probability one half" (see Smets (1991, p. 12) and Dixit and Pindyck (1996, p. 313)) need not be true.

The point we make here extends to other contributions that include the real option framework in duopoly models. These papers, such as Grenadier (1996), Dutta et al. (1995), and Weeds (2002), make unsatisfactory assumptions with the aim to be able to ignore the possibility of simultaneous investment at points of time that this is not optimal. Grenadier (1996, pp. 1656-1657) assumes that "if each tries to build first, one will randomly (i.e., through the toss of a coin) win the race", while Dutta et al. (1995, p.568) assume that "If both [firms] i and j attempt to enter at any period t, then only one of them succeeds in doing so".