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Essays on Innovation and Contest Theory Zurich Open Repository and Archive University of Zurich Main Library Strickhofstrasse 39 CH-8057 Zurich www.zora.uzh.ch Year: 2017 Essays on innovation and contest theory Letina, Igor Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-136322 Dissertation Published Version Originally published at: Letina, Igor. Essays on innovation and contest theory. 2017, University of Zurich, Faculty of Economics. Essays on Innovation and Contest Theory Dissertation submitted to the Faculty of Business, Economics and Informatics of the University of Zurich to obtain the degree of Doktor der Wirtschaftswissenschaften, Dr. oec. (corresponds to Doctor of Philosophy, PhD) presented by Igor Letina from Bosnia and Herzegovina approved in February 2017 at the request of Prof. Dr. Armin Schmutzler Prof. Dr. Nick Netzer Prof. Dr. Georg Nöldeke The Faculty of Business, Economics and Informatics of the University of Zurich hereby autho- rizes the printing of this dissertation, without indicating an opinion of the views expressed in the work. Zurich, 15.02.2017 Chairman of the Doctoral Board: Prof. Dr. Steven Ongena iv Acknowledgements When it comes to achievements, research suggests that individuals tend to underestimate the role of luck and to overestimate the contribution of their own effort and abilities. Even with that bias, I am amazed by the amount of good fortune that I have had while writing this thesis. I was fortunate to have advisors who were generous with their time and advice and gentle but precise with their criticism. Without the kind guidance of Nick Netzer, Georg Nöldeke and in particular Armin Schmutzler, the quality of this dissertation, and the person submitting it, would be significantly lower. Writing a thesis is a process filled with uncertainty and self-doubt. For me, it would have been an impossible task without the amazing colleagues from the University of Zurich. In particular I would like to thank Jean-Michel Benkert, Lea Cassar, Florian Engl, Tobias Gesche, Andreas Hefti, Steve Heinke, Stefan Jönsson, Arnd Heinrich Klein, Johannes Kunz, Shuo Liu, Andràs Péchy, Philippe Ruh and Sabrina Studer. For their support and trust in me, I am grateful to my parents Desanka and Aleksandar Letina, and to my brother Srđan Letina. Last but not least, I am thankful to my co-authors. Jean-Michel Benkert, Shuo Liu, Nick Netzer and Armin Schmutzler, it was a joy working with you. Igor Letina, Zurich, November 2016 v vi Contents I Dissertation Overview 1 II Research Papers 7 1 The Road not Taken: Competition and the R&D Portfolio 9 1.1 Introduction . 9 1.2 Related literature . 11 1.3 A model of stochastic multiproject innovation . 13 1.4 Equilibrium . 16 1.5 Comparative statics . 19 1.6 Optimal portfolio . 23 1.7 Extensions and robustness . 27 1.8 Conclusion . 30 2 Inducing Variety: A Theory of Innovation Contests 33 2.1 Introduction . 33 2.2 The Model . 37 2.3 The Optimal Contest for the Buyer . 39 2.3.1 Auxiliary Results . 39 2.3.2 Characterizing the Optimum . 41 2.4 Auctions and Fixed Prize Tournaments . 43 2.5 Extensions . 45 2.5.1 Number of Suppliers . 45 2.5.2 Other Extensions . 47 2.5.2.1 Generalized distributions and quality functions. 47 2.5.2.2 Heterogeneous Suppliers . 48 2.5.2.3 Fixed-Prize Tournaments with Multiple Prizes . 49 2.5.2.4 Multiple Designs by the Same Supplier . 49 2.6 Relation to the Literature . 50 2.7 Conclusions and Discussion . 52 3 Designing Dynamic Research Contests 55 3.1 Introduction . 55 3.2 Related Literature . 58 3.3 The Model . 61 vii viii 3.4 Optimal Contest . 63 3.5 Robustness . 66 3.6 Conclusion . 68 4 Delegating Performance Evaluation 71 4.1 Introduction . 71 4.2 The Model . 76 4.2.1 Environment . 76 4.2.2 Implementation with Credible Contracts . 77 4.3 Optimal Contracts . 79 4.3.1 The Optimality of Contests . 79 4.3.2 Optimal Contests . 82 4.3.3 Unique Implementation . 83 4.3.4 Implementation in Tullock Contests . 84 4.4 Extensions . 85 4.4.1 Imperfect Effort Observation . 85 4.4.2 Cheap Talk . 87 4.4.3 Non-Separability and Asymmetry . 88 4.5 Related Literature . 90 4.6 Conclusion . 93 III Appendices 95 A Appendix: Chapter 1 97 A.1 Main Proofs and the Running Example . 97 A.1.1 Proof of Proposition 1.1 . 97 A.1.2 Proof of Proposition 1.2 . 101 A.1.3 Proof of Proposition 1.3 . 102 A.1.4 Proof of Proposition 1.4 . 102 A.1.5 Proof of Proposition 1.5 . 103 A.1.6 Proof of Corollary 1.1 . 104 A.1.7 Proof of Proposition 1.6 . 104 A.1.8 Proof of Corollary 1.2 . 105 A.1.9 Proof of Proposition 1.7 . 105 A.1.10 Example: Process innovation in a Cournot market . 106 A.2 Further Extensions . 108 A.2.1 Efficiency defense . 108 A.2.2 Mixed strategies . 111 A.2.3 Limited budget and costly financing . 111 A.2.4 Proof of Proposition A.1 . 113 A.2.5 Proof of Proposition A.2 . 115 A.2.6 Proof of Proposition A.3 . 116 A.2.7 Proof of Proposition A.4 . 117 ix B Appendix: Chapter 2 119 B.1 Basics . 119 B.1.1 Notation . 119 B.1.2 Subgame-Perfect Equilibrium . 119 B.2 Proofs of Auxiliary Results (Section 2.3.1) . 120 B.2.1 Proof of Lemma 2.1 . 120 B.2.2 Proof of Lemma 2.2 . 121 B.2.3 Proof of Lemma 2.3 . 122 B.3 Proofs of Main Optimality Results (Section 2.3.2) . 122 B.3.1 Proof of Proposition 2.1 . 122 B.3.2 Proof of Theorem 2.1 . 122 B.3.3 Proof of Corollary 2.1 . 127 B.4 Proofs on Auctions and Tournaments (Section 2.4) . 127 B.4.1 Proof of Proposition 2.2 . 127 B.4.2 Proof of Corollary 2.3 . 128 B.5 Extensions: n > 3 (Section 2.5.1) . 129 B.5.1 Proof of Lemma 2.4 . 129 B.5.2 Sufficient Conditions for FPT equilibria . 131 B.5.3 Proof of Proposition 2.3 . 131 B.5.4 Proof of Corollary 2.4 . 132 B.6 Other Extensions (Section 2.5.2) . 132 B.6.1 Proof of Corollary 2.5 . 132 B.6.2 Proof of Proposition 2.4 . 133 B.6.3 Proof of Lemma 2.5 . 134 C Appendix: Chapter 3 137 C.1 Proof of Proposition 3.1 . 137 C.2 Proof of Proposition 3.2 . 139 C.3 Proof of Proposition 3.3 . 139 C.4 Proof of Proposition 3.4 . 139 C.5 Proof of Proposition 3.5 . ..
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