Topics of Principal-Agent Contracts: Contract Analysis and Pooling Principals Item Type text; Electronic Dissertation Authors Zeng, Shuo Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 29/09/2021 22:40:31 Link to Item http://hdl.handle.net/10150/577498 Topics of Principal-Agent Contracts: Contract Analysis and Pooling Principals by Shuo Zeng ||||||||||||| A Dissertation Submitted to the Faculty of the Department of Management Information Systems In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy In the Graduate College The University of Arizona 2015 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Shuo Zeng, titled Topics of Principal-Agent Contracts: Contract Analysis and Pooling Principals, and recommend that it be accepted as fulfilling the dissertation require- ment for the Degree of Doctor of Philosophy. Date: 8/7/2015 Professor Moshe Dror Date: 8/7/2015 Professor Paulo Goes Date: 8/7/2015 Professor Stanley Reynolds Final approval and acceptance of this dissertation is contingent upon the candidates submis- sion of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recom- mend that it be accepted as fulfilling the dissertation requirement. Date: 8/7/2015 Dissertation Director: Professor Moshe Dror 2 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of the requirements for an ad- vanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that an accurate acknowledgement of the source is made. Requests for permission for ex- tended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Shuo Zeng 3 ACKNOWLEDGEMENTS I would never have been able to finish this dissertation without the guidance from many great scholars, help from friends, and understanding and support from my family. It is my pleasure to thank all those who make this dissertation possible. Foremost, I would like to express my most profound thanks to my advisor, Dr. Moshe Dror, for his continuous encouragement, excellent guidance, and tremendous support through- out my doctoral study. I deeply appreciate his decision to accept me as his doctoral student, his generosity in spending time on me, and his optimism and confidence in me. I will always be indebted to him for his comments on countless revisions of my dissertation, and for his advice on the rehearsal for all my research presentations. He is one of my best mentors and I will definitely benefit a lot from his training in my future career. I am grateful to my dissertation committee members, Dr. Paulo Goes and Dr. Stanley Reynolds, for their contributions and their helpful comments. I am also grateful to the late Dr. Moshe Shaked, who untimely passed away in October 2014, for his generosity in sharing his time and knowledge with me during the creation of the first part of my dissertation. I would like to thank the following faculty members and staffs from the Eller College of Management at the University of Arizona for their various forms of support and advice dur- ing the years of my study: Dr. Hsinchun Chen, Dr. Mingfeng Lin, Dr. Nichalin Suakkaphong Summerfield, Dr. Mark Patton, Dr. William Neumann, Dr. Mark Stegeman, Cinda Van Winkle, Mary Lambert, and Cathy Larson. I would also like to thank Dr. Xin Li and Dr. Yida Chen for their emotional support. Finally and most importantly, my career would never have reached this new height with- out the love and support from my family. I am deeply grateful to my parents for their unconditional love and care, and for being there whenever I need them. I am also deeply grateful to my wife, Michelle, for her love, understanding, support, and patience. I am lucky to have all of you in my life. 4 DEDICATION I dedicate my doctoral dissertation to my mother Xiumin Du and my father Ming Zeng, who have always taught me to never give up and have been supporting me unconditionally in all possible ways, especially during the most difficult times of this long journey. I also dedicate my work to my wife, Michelle, whose love and support sustained me throughout my doctoral study. 5 Contents List of Figures ...................................... 9 List of Tables ....................................... 11 Abstract .......................................... 12 1 Introduction ...................................... 14 2 Formulating Principal-Agent Service Contracts for a Revenue Generat- ing Unit ........................................ 15 3 The Basic Principal-Agent ............................. 17 3.1 Contractual relationship between a principal and an agent . 21 4 Risk-Neutral Agent ................................. 24 4.1 Optimal strategies for risk-neutral agent . 25 4.1.1 Sensitivity analysis of the optimal strategy . 31 4.1.2 The second-best solution . 32 4.1.3 Our principal-agent game . 34 5 Risk-Averse Agent .................................. 35 5.1 Optimal strategies with a weakly risk-averse agent . 38 5.1.1 Sensitivity analysis of a weakly risk-averse agent's optimal strategy . 53 5.1.2 Principal's optimal strategy . 57 5.2 Optimal strategies given a strongly risk-averse agent . 70 5.2.1 Sensitivity analysis of a strongly risk-averse agent's optimal strategy . 80 5.2.2 Principal's optimal strategy . 83 5.3 Risk-averse agent { a summary . 88 5.3.1 Sensitivity analysis of optimal strategies in high revenue industry . 90 5.3.2 The second-best solution in high revenue industry . 92 6 Risk-Seeking Agent ................................. 93 6 6.1 Optimal strategies for the weakly risk-seeking agent . 97 6.1.1 Sensitivity analysis of a weakly risk-seeking agent's optimal strategy . 113 6.1.2 Principal's optimal strategy . 116 6.2 Optimal strategies for the moderately risk-seeking agent . 125 6.2.1 Sensitivity analysis of a moderately risk-seeking agent's optimal strategy135 6.2.2 Principal's optimal strategy . 137 6.3 Optimal strategies for the strongly risk-seeking agent . 141 6.4 Risk-seeking agent { a summary . 143 7 Summary: Formulating Principal-Agent Service Contracts for a Revenue Generating Unit ................................... 145 7.1 Interpreting Table 7.1 . 148 8 Pooling Principals .................................. 150 8.1 An outline . 152 9 Principal-Agent Model with Multiple Principals ............... 153 9.1 The principal-agent model . 156 9.2 Performance based contract and the agent's profit . 158 9.3 Principal's profit . 159 10 Selecting Principals Set N ............................. 160 10.1 Selecting a finite set of homogeneous principals . 160 10.1.1 Selecting two principals under FCFS queuing discipline . 161 10.1.2 Selecting two principals under HOLP queuing discipline . 164 10.2 Selecting a finite set of heterogeneous principals . 166 10.3 Simulation results . 167 10.3.1 Simulation results with homogeneous principals . 169 10.3.2 Simulation results with heterogeneous principals . 174 10.4 When to stop pooling principals? . 177 11 Serving Principals Set N .............................. 179 7 11.1 Principal-agent model with perfectly negative dependencies . 179 12 Principal-Agent: The Cooperative Game Perspective ............ 182 12.1 Each principal's `fair contribution' . 189 13 Summary: Pooling Principals ........................... 194 14 A Comparison of Performance Based Service Contracts .......... 196 References ......................................... 199 8 List of Figures 4.1 Illustration of the forms of u(µ) ......................... 27 4.2 Structure of the proof for Proposition 4.3 . 27 4.3 Conditions when a risk-neutral agent accepts the contract . 29 4.4 Structure of the proof for Theorem 4.4 . 30 4.5 Structure of the principal-agent extensive form game . 34 5.1 π(µ, w; p) as a function of P (1) when η =1................... 37 5.2 Illustration of the forms of u(µ) when η 2 (0; 3=5] . 46 5.3 Structure of the proof for Proposition 5.9 when η 2 (0; 3=5] . 47 5.4 Illustration of the forms of u(µ) when η 2 (3=5; 4=5) . 50 5.5 Structure of the proof for Proposition 5.9 when η 2 (3=5; 4=5) . 51 5.6 Conditions when a weakly risk-averse agent accepts the contract with η = 0:6 54 5.7 Structure of the proof for Proposition 5.18 . 64 5.8 Structure of the proof for Theorem 5.19 and Proposition 5.20 . 69 ~ ∗ ∗ ∗ ∗ ∗ ∗ 5.9 The value of ΠP ≡ ΠP (w ; p = pcu; µ ) − ΠP (w ; p = p3; µ ) for r 2 (p3; r2) . 71 5.10 Illustration of the forms of u(µ) when η 2 [4=5; 1) . 74 5.11 Structure of the proof for Proposition 5.23 when η 2 [4=5; 1) . 75 5.12 Illustration of the forms of u(µ) when η ≥ 1................... 78 5.13 Structure of the proof for Proposition 5.23 when η ≥ 1 . 79 5.14 Conditions when a strongly risk-averse agent accepts the contract with η = 2 81 5.15 Structure of the proof for Theorem 5.27 . 86 5.16 Conditions when a risk-neutral principal makes offers to a risk-averse agent .