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The Dynamics of Europe's Political Economy Die approbierte Originalversion dieser Dissertation ist in der Hauptbibliothek der Technischen Universität Wien aufgestellt und zugänglich. http://www.ub.tuwien.ac.at The approved original version of this thesis is available at the main library of the Vienna University of Technology. http://www.ub.tuwien.ac.at/eng DISSERTATION The Dynamics of Europe’s Political Economy: a game theoretical analysis Ausgeführt zum Zwecke der Erlangung des akademischen Grades einer Doktorin der Sozial- und Wirtschaftswissenschaften unter der Leitung von Univ.-Prof. Dr. Hardy Hanappi Institut für Stochastik und Wirtschaftsmathematik (E105) Forschunggruppe Ökonomie Univ.-Prof. Dr. Pasquale Tridico Institut für Volkswirtschaftslehre, Universität Roma Tre eingereicht an der Technischen Universität Wien Fakultät für Mathematik und Geoinformation von Mag. Gizem Yildirim Matrikelnummer: 0527237 Hohlweggasse 10/10, 1030 Wien Wien am Mai 2017 Acknowledgements I would like to thank Professor Hardy Hanappi for his guidance, motivation and patience. I am grateful for inspirations from many conversations we had. He was always very generous with his time and I had a great freedom in my research. I also would like to thank Professor Pasquale Tridico for his interest in my work and valuable feedbacks. The support from my family and friends are immeasurable. I thank my parents and my brother for their unconditional and unending love and support. I am incredibly lucky to have great friends. I owe a tremendous debt of gratitude to Sarah Dippenaar, Katharina Schigutt and Markus Wallerberger for their support during my thesis but more importantly for sharing good and bad times. I also would like to thank Gregor Kasieczka for introducing me to jet clustering algorithms and his valuable suggestions. Abstract Coalition formation models lie at the intersection of political science and economics. They deal with the creation of groups amongst agents as well as the determination of the outcome of many social, economic and political interactions. Although coalition formation is a well studied concept in the domain of economics, particularly in game theory, most models focus on a stable outcome and the process of coalition formation has received less attention. Indeed, the process of coalition formation is the point of departure of my research. The main goal of this thesis is to investigate the process of coalition formation with a focus on international agreements and the dynamics of Europe’s political economy. Two game-theoretical coalition formation models are built and tailored to the EU and international coalitions in general. One of the aims is to establish links between theoretical models and applications thereby getting a better under standing of dynamics of the EU. While the first model uses a sequential approach in which players iteratively form subcoalitions, the second model uses a simultaneous approach in which players form coalitions at once with all members. The sequential algorithm for coalition formation is inspired by the study of jets in high energy physics experiments and the simultaneous model is inspired by correlation clustering in computer science. There are two main considerations. The first one is the computational complexity of coalition formation processes. The computational aspects of coalition formation games are of increased importance as these games are used to analyze situations with numerous players. However, in economics and political science there are limited number of analyses concerning with this issue. The second consideration is the determination of the distance between players. The majority of theoretical works in the literature assume a geometrical distance function in the Euclidean space. The examination of different distance functions and their role in shaping coalitions is the subject of this research. The distance between two countries is measured by a distance function which has geometrical element, geographical distance, and non-geometrical elements, GDP, GDP per capita, population and regime type. Python implementations of coalition formation algorithms are presented. The results including data from 28 European countries illustrate the impact of the distance function in the process. Both models predict five founder member states (with the exception of Italy) of the EU. The presented thesis is an interdisciplinary work. It is devoted to the questions of which coalitions will be formed, how one defines the distance between players, how resulting coalitions intertwine with the process and how to reduce the computational complexity of the process. vi Zusammenfassung Die theoretische Auseinandersetzung mit und Modellierung von Koalitionsmodellen erfolgt an der Schnittstelle von Politik- und Wirtschaftswissenschaften. Kern der Betrachtung sind dabei meist die Zusammenschlüsse einzelner Koalitionäre - wie hier z.B. Staaten - und die Ziele ihrer sozialen, wirtschaftlichen und politischen Interessen und Interaktionen. Wenngleich Koalitionen einen ausführlich untersuchten Bereich innerhalb der Wirtschaftswis- senschaften, speziell der Spieltheorie, darstellen, so liegt der Fokus dabei meist auf dem Erreichen eines stabilen Gleichgewichts. Dem zugrundeliegenden Prozess der Koalitionsbil- dung wurde bisher nur wenig Bedeutung beigemessen. Dies bildet den Ausgangspunkt der vorliegenden Arbeit. Ein solcher Prozess wird anhand internationaler Übereinkommen, unter besonderer Berücksichtigung der Dynamik der Politischen Ökonomie Europas, näher untersucht. Hi- erfür werden zwei spieltheoretische Modelle entworfen und die Bildung von Koalitionen anhand eines internationalen Staatenbündnisses auf europäischer Ebene angewendet. Zwei Anwendungsbeispiele der Modelle ermöglichen dabei besseres Verständnis für die Dynamik innerhalb der Europäischen Union. Das erste Modell mit sequentiellem Ansatz lässt die SpielerInnen schrittweise Subkoalitionen bilden, während das zweite Modell mit simultanem Ansatz die SpielerInnen zu einem bestimmten Zeitpunkt eine Koalition formen lässt. Der sequentielle Ansatz hat seinen Ursprung in Experimenten der Hochenenergiephysik mit soge- nannten "Jets"; der simultane Ansatz basiert auf korrelationsgesteuerte Clustering-Methoden der Computerwissenschaft. Die Zielsetzung dieser Arbeit umfasst zwei wesentliche Aspekte: die Rechenkomplexität bei der Modellierung von Koalitionsbildungsprozessen sowie die Bedeutung der Distanzfunk- tion. Die Rechenkomplexität im Rahmen der Modellierung von Koalitionsbildungsprozessen. Diese ist von steigender Bedeutung, da anhand einzelner Spiele Koalitionen mit zahlreichen SpielerInnen berechnet werden. In den Wirtschafts- und Politikwissenschaften haben sich bisher jedoch nur wenige Studien mit diesem Problem auseinandergesetzt. Der zweite wesentliche Teil dieser Arbeit ist die Beschäftigung mit der Abstandsfunktion zwischen den einzelnen SpielerInnen. In der Literatur wird derzeit mit überwiegender Mehrheit die Euklidsche Abstand angenommen. In der vorliegenden Arbeit werden verschiedene Dis- tanzfunktionen und ihre Rolle in der Koalitionsbildung betrachtet. Die Distanz zwischen zwei SpielerInnen - hier Staaten - wird anhand einer Distanzfunktion abgebildet, die ge- ographische, geometrische und nicht-geometrische Größen, wie das Bruttoinlandsprodukt, das Pro-Kopf-Bruttoinlandsprodukt, die Bevölkerungsgröße wie auch der Art der Regime- Typen miteinbezieht. Die entwickelten Algorithmen werden in Python implementiert und die Ergebnisse in der Arbeit präsentiert. Diese umfassen Daten aus 28 Staaten und zeigen den Einfluss der Distanzfunktion auf den Prozess der Koalitionsbildung. Beide der angewendeten Modelle berechnen – mit Ausnahme von Italien – fünf der sechs Gründerstaaten der Europäischen Union voraus. Der in dieser Arbeit vorgestellte interdisziplinäre Zugang strebt die Beantwortung mehrerer grundlegender Fragen an: Welche Koalitionen werden gebildet? Wie wird die Distanz zwischen einzelnen SpielerInnen definiert? Welchen Zusammenhang gibt es zwis- chen den gebildeten Koalitionen und dem ihnen zugrundeliegenden Prozess? Wie kann die Berechnungskomplexität in der Modellierung eines solchen Prozesses reduziert werden? viii Table of contents List of figures xiii List of tables xv 1 Introduction1 2 Coalition Formation5 2.1 Forming Coalitions . .7 2.2 Preferences . 13 2.2.1 Restrictions on Preferences . 13 2.2.2 One-dimensional versus Multi-dimensional models . 20 2.2.3 Cardinal and Ordinal Preferences . 22 2.2.4 Forming a coalition with neighbors . 25 2.2.5 Fixed and changing preferences . 26 2.3 Process . 27 2.4 Stability - Why so much Stability . 30 3 Clustering 33 3.1 Similarity and distance function . 34 3.2 Clustering algorithms . 35 3.2.1 Computational Complexity . 36 4 The EU and International Coalitions 39 4.1 A Brief History of the EU . 39 4.2 Coalition Formation in the EU . 40 Table of contents 4.3 Data . 43 The Dynamics of Europe’s Political Economy: a game theoretic analysis 48 5 Sequential Coalition Formation 51 5.1 Sequential Coalition Formation . 53 5.2 Model . 57 5.2.1 Coalition formation depends on only geographical location and regime type . 62 5.2.2 A general coalition formation . 64 5.2.3 Computational Complexity . 65 5.3 Application . 69 5.3.1 Geographical pattern of coalition formation . 70 5.3.2 General Case . 73 6 Simultaneous Coalition Formation 81 6.1 Correlation Clustering . 81 6.2 Clustering Games . 84 6.3 Model . 85 6.3.1 Coalition formation depends on location . 91 6.3.2 A general coalition formation . 92 6.3.3 Computational Complexity . 93 6.4 Application
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