Rank order tournaments as selection mechanisms [Elektronische Ressource] : applications in project finance / vorgelegt von Cornelia Kaldewei

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• Management

Informations

• Publié par: eberhard_karls_universitat_tubingen
• Publié le: 01 janvier 2007
• Nombre de lectures: 8
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

RANK-ORDER TOURNAMENTS AS SELECTION
MECHANISMS:
APPLICATIONS IN PROJECT FINANCE
Inaugural-Dissertation
zur Erlangung des Doktorgrades
an der Wirtschaftswissenschaftlichen Fakult¨at
der Eberhard-Karls-Universit¨at Tu¨bingen
vorgelegt von
Cornelia Kaldewei
aus Dortmund
2007Dekan: Prof. Dr. Joachim Grammig
Erstkorrektor: Prof. Dr. Uwe Walz
Zweitkorrektor: Prof. Dr. Manfred Stadler
Tag der mu¨ndlichen Pru¨fung: 25. April 2007
iiTable of Contents
Table of Contents iii
List of Figures vi
1 Introduction 1
2 Rank-order tournaments 13
2.1 The basic tournament model . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Existence and properties of equilibria in tournaments . . . . . . . . . 19
2.2.1 Risk aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Heterogeneity of contestants . . . . . . . . . . . . . . . . . . 23
2.2.3 Multiple contestants and prizes . . . . . . . . . . . . . . . . . 30
2.3 Fields of application and empirical findings . . . . . . . . . . . . . . 40
2.3.1 Fields of application . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.2 Empirical findings. . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4 Selection properties of tournaments . . . . . . . . . . . . . . . . . . . 52
2.4.1 Selection with and without private information . . . . . . . . 53
2.4.2 A tournament model with selection properties and private in-
formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.3 Some further considerations on selection efficiency . . . . . . 65
3 Common value auction with asymmetric information 67
3.1 The Engelbrecht-Wiggans and others (1983) model . . . . . . . . . . 71
3.1.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.1.2 Equilibrium bidding strategies . . . . . . . . . . . . . . . . . . 73
3.2 Applications of the Engelbrecht-Wiggans and others (1983) model . . 78
3.2.1 Empirical findings . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.2 An application to finance . . . . . . . . . . . . . . . . . . . . . 80
iii4 Internal capital markets, information revelation and corporate auc-
tions 84
4.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.1 Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.2 Technology and information . . . . . . . . . . . . . . . . . . . 93
4.1.3 Common value auction and information acquisition . . . . . . 96
4.1.4 Equilibrium analysis: why the division with the lower quality
signal will be divested . . . . . . . . . . . . . . . . . . . . . . 97
4.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1 Equilibrium strategies in the corporate auction . . . . . . . . 100
4.2.2 Equilibrium expected payoffs after the corporate auction . . . 105
4.2.3 Equilibrium in the internal capital market . . . . . . . . . . . 110
4.3 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.1 Effects of parameter changes on equilibrium effort levels . . . 115
4.3.2 Effects of parameter changes on equilibrium bids in the corpo-
rate auction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.3 Effects of parameter changes on expected payoffs . . . . . . . 124
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 Business plan contests, information revelation and financing deci-
sions 138
5.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.1.1 Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.1.2 Technology and information . . . . . . . . . . . . . . . . . . . 149
5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2.1 Equilibrium strategies in the financing game . . . . . . . . . . 153
5.2.2 Equilibrium expected payoffs from the financing game . . . . . 158
5.2.3 Equilibrium in the business plan contest . . . . . . . . . . . . 162
5.3 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.3.1 Effects of parameter changes on equilibrium effort levels . . . 166
5.3.2 Effects of parameter changes on equilibrium bids in the financ-
ing game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.3.3 Effects of parameter changes on expected payoffs . . . . . . . 177
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
6 Conclusion 187
ivA Appendix to chapter 4 196
A.1 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 196
A.2 Determination of Pr{win} and Pr{MBO} . . . . . . . . . . . . . . 206
A.3 The expected bid of the uninformed investor, conditional on winning
the corporate auction . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
A.4 Second order condition for the optimal effort decision . . . . . . . . . 209
A.5 Effects of parameter changes on Pr{MBO} . . . . . . . . . . . . . . 210
A.6 Effects of parameter changes on bidding strategies . . . . . . . . . . . 211
B Appendix to chapter 5 214
B.1 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 214
B.2 The expected bid of the outside investor, conditional on winning the
financing game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
B.3 Second order condition for the optimal effort decision . . . . . . . . . 225
B.4 Effects of parameter changes on bidding strategies . . . . . . . . . . . 226
Bibliography 230
vList of Figures
4.1 Internal capital market: stages . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Manager A’s reaction function r = x (x ) . . . . . . . . . . . . . . 113A A B
∗ ∗ ∗4.3 Equilibrium effort levels x = x = x . . . . . . . . . . . . . . . . . 114A B
4.4 Equilibrium effort levels for different α and v . . . . . . . . . . . . . . 115
4.5 Equilibrium effort levels for different γ and v . . . . . . . . . . . . . . 117
4.6 Equilibrium effort levels for different v . . . . . . . . . . . . . . . . . 119
4.7 Internal capital market: comparative statics . . . . . . . . . . . . . . 132
5.1 Business plan contest: stages . . . . . . . . . . . . . . . . . . . . . . . 152
5.2 Entrepreneur A’s reaction function r = x (x ) . . . . . . . . . . . 164A A B
∗ ∗ ∗5.3 Equilibrium effort levels x = x = x . . . . . . . . . . . . . . . . . 165A B
5.4 Equilibrium effort levels for different α and μ . . . . . . . . . . . . . 166g
5.5 Equilibrium effort levels for different γ and μ . . . . . . . . . . . . . 169g
5.6 Equilibrium effort levels for different μ . . . . . . . . . . . . . . . . . 171g
5.7 Business plan contest: comparative statics . . . . . . . . . . . . . . . 182
A.1 Divestiture matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
A.2 Tournament probability tree . . . . . . . . . . . . . . . . . . . . . . . 203
B.1 Winning matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
viB.2 Contest probability tree . . . . . . . . . . . . . . . . . . . . . . . . . 220
viiChapter 1
Introduction
Tournaments are a fact of life. They are used to rank athletes in sports events, work-
erscompetingforapromotion,andoffersforgovernmentprocurementcontracts. The
realm of applications for tournaments is virtually limitless, given that in almost every
aspect of life, ranking decisions of some sort or another have to be made.
Part of what makes rank-order tournaments or contests so appealing is their rela-
tivelylowinformationalrequirement. Inaworldofcompleteandperfectinformation,
rewards for achievements or for certain characteristics could be distributedon the ba-
sis of absolute input or output measures. However, if such cardinal ranking is costly
or even impossible because it calls for costly monitoring or screening activities, or
because certain traits simply cannot be compared on a cardinal scale (as, for exam-
ple, in beauty contests), rank-order tournaments can prove to be superior selection
or incentive mechanisms in the face of incomplete or imperfect information. Building
on the well-known principal-agent paradigm, which is also concerned with the pro-
vision of incentives and selection mechanisms in the face of imperfect or incomplete
information, tournaments are useful mechanisms in multiple-agent settings. In that,
12
they are closely related to auctions. Indeed, a specific type of auction, the first-price
all-pay auction, is often used to model tournament applications.
While the theoretical tournament literature has long focused on analyzing in-
centive effects for homogeneous contestants, or for heterogeneous contestants with
complete information, this thesis explores the potential of tournaments as selection
devices in the context of heterogeneous competitors and incomplete information. It
develops two applications in the field of finance, where managers/entrepreneurs com-
pete over the allocation of scarce resources. In the first application, two division
managers compete over limited funds in a conglomerate’s internal capital market. In
the second application, two entrepreneurs compete in a business plan contest, spon-
sored by a venture capitalist.
Themainfocusofthisthesisison“selectionefficiency”, definedastheprobability
with which the best contestant is picked as the tournament winner. In particular,
both applications restrict contestants’ actions to pure signaling activities, thus avoid-
ing a