DOCTORAL THESIS Conformists and Anti-conformists in Opinion Formation and Diffusion Author: Supervisors: Fen LI Prof. Michel Grabisch Prof. Herbert Dawid A thesis submitted in fulfillment of the requirements for the degree of Doctor of Applied Mathematics of CES - Centre d’économie de la Sorbonne, University of Paris 1 Panthéon Sorbonne; and Doctor of Economics of the Faculty of Business Administration and Economics, Bielefeld University. Date of defense: December 16, 2020 ii EXAMINATION COMMITTEE Berno Buechel University of Fribourg Referee Herbert Dawid University of Bielefeld Advisor Michel Grabisch University of Paris 1 Panthéon Sorbonne Advisor Tim Hellmann University of Southampton Examiner Katarzyna Sznajd-Weron Wroclaw University of Science and Technology Referee Curriculum Vitae Fen LI Gender: Female Date of birth: May 11, 1993 0033(0)769438066 Place of birth: Shandong, China 28 Rue Michelet Nationality: Chinese 54000, Nancy, France Email: [email protected] Current Position 2017- Early Stage Researcher & PhD candidate Innovative Training Network ’Expectations and Social Influence Dynamics in Economics’ (ExSIDE) 1. Université Paris 1 Panthéon-Sorbonne & Bielefeld University. Project: Conformists and Anticonformists in Opinion Formation and Diffusion; Supervisors: Michel Grabisch, Herbert Dawid . Research Interests Decision Making, Game Theory, Opinion Dynamics in Networks, Anti-conformism Education 2016-2017 MMMEF master 2, Université Paris 1 Panthéon-Sorbonne, Paris, France M2 in Mathematical Economics, Games and Decision. GPA: 4/4. Master 2 Thesis: A Pólya Urn Model of Opinion Formation. 2013-2016 Ocean University of China (OUC), Qingdao, Shandong, China M.S. in Probability Theory and Statistics, 2016 Outstanding Master of Ocean University of China. Master thesis: Global Sensitivity Analysis of Marine Ecosystem Dynamics Models based on the Morris Method and the Sobol Method 2009-2013 Ocean University of China (OUC), Qingdao, Shandong, China B.S. in Applied Mathematics, summa cum laude. Undergraduate thesis: Optimization on the Reduction of Major Pollutants of Laizhou Bay 1This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 721846. See http://exside-itn.eu/ Fen LI 2 Conferences, Workshops, Summer Schools 11/2020 Statistical Physics in Complex Systems (SPiCy) seminar via zoom, organized by Wroclaw University of Science and Technology. Presentation entitled Continuous opinion dynamics with anti-conformity behavior. 09/2020 Network Group Seminar, Paris, France. Presentation entitled Continuous opinion dynamics with anti-conformity behavior. 07/2020 Intelligent Control Series Report via zoom, organized by Peking University. Presentation entitled Continuous opinion dynamics with anti-conformity behavior. 12/2019 International workshop on "Network approach to opinion formation and interaction", Paris, France. Presentation entitled The Transmission of Continuous Cultural Traits in Endogenous Social Networks. 11/2019 Ordered Structures in Games and Decisions 13th seminar day, Paris. 11/2019 Visit to the Department of Mathematical Sciences at Politecnico di Torino. Workshop "Net- work Dynamics in the Social, Economic, and Financial Sciences". Seminars at DISMA Work- shops. 07/2019 30th International Conference on Game Theory at Stony Brook, U.S. Presentation entitled Anti-conformism in the threshold model of collective behavior. 07/2019 Summer School "Equilibria in Financial Markets: General Equilibrium and Game Theoretic Perspective" at Bielefeld University, Bielefeld, Germany. 04/2019 Network Science in Economics Conference at Indiana University-Bloomington, U.S. Presen- tation entitled Anti-conformism in the threshold model of collective behavior. 10/2018 The Lisbon Meetings in Game Theory and Applications. Presentation entitled Opinion Dy- namics with Anti-conformist agents. 07/2018 The 14th European (formerly Spain-Italy-Netherlands) Meeting on Game Theory (SING14), Bayreuth, Germany. Presentation entitled Opinion Dynamics with Anti-conformist agents. 05/2018 Deliberation, Belief Aggregation, and Epistemic Democracy, Paris, France. 04/2018 23rd Coalition Theory Network Workshop, Maastricht, Netherlands. 11/2017 Ordered Structures in Games and Decision, Paris, France. 12/2017 Journées Internes Aussois, Aussois, France. Poster entitled A Pólya Urn Model of Opinion Formation. 07/2015 Summer school of the 3rd International Marine Frontier Research under funding support 09/2014 The 4th Australia - China Ocean Science & Technology Symposium (ACOST4). Presentation entitled Distribution of Phytoplankton Biodiversity in relations to environmental variables in South- five island of Miaodao Archipelago. 11/2013 The 2013 national doctoral student academic forum. Submitted the abstract of Laizhou bay regulate control and optimize of pollution Papers Published [1] Grabisch, M., Li, F. Anti-conformism in the Threshold Model of Collective Behavior. Dyn Games Appl 10, 444 - 477 (2020). https://doi.org/10.1007/s13235-019-00332-0. [2] Zheng W, Li F, Shi H, et al. Spatiotemporal heterogeneity of phytoplankton diversity and its re- lation to water environmental factors in the southern waters of Miaodao Archipelago, China. Acta Oceanologica Sinica, 2016, 35. [3] Shen C, Shi H, Zheng W, Li F, Peng S, Ding D. Study on the cumulative impact of reclamation activities on ecosystem health in coastal waters. Marine Pollution Bulletin, 2016, 103(1-2): 144-150. Fen LI 3 [4] Shen C, Shi H, Liu Y, Li F, Ding D. Discussion of skill improvement in marine ecosystem dynamic models based on parameter optimization and skill assessment. Chinese Journal of Oceanology and Limnology, 2015:1-14. [5] Shi H, Shen C, Wang X, Li F, Chi Y, Guo Z, Qiao M, Gao L, Ding D. Amodel to assess fundamental and realized carrying capacities of island ecosystem: a case study in the southern Miaodao Archipelago of China. Acta Oceanologica Sinica, 2016, 35(2): 56-67. [6] LI F, Shen C, Shi H, Chi Y, Guo Z, Ding D. Uncertainty analysis on ecosystem-based carrying capacity of island: A case study in the Southern Island Group of Miaodao Archipelago Marine Envi- ronmental Science, 2016, 35(4): 481-488. (in Chinese) [7] Shi H, Shen C, Li F, Wang Y. Jiaozhou Bay biology - Sensitivity analysis on physics coupling model parameter. Acta Ecologica Sinica, 2014, 34(1): 41-49. (in Chinese) Awards and honors Academic 2015 Zhang Zidao Island Outstanding Student Scholarship Awarded by Ocean University of China. This scholarship was rated based on academic and research activity 80%, academic performance 10%, innovative undertaking and social activities 10% 2015 2nd prize on academic forum of school of mathematical science of OUC. Awarded by Ocean University of China 2014 Academic Scholarship of OUC Awarded by Ocean University of China. (Ranking top 3 in academic performance and excellent in researching area.) 2014 Outstanding graduate student of OUC Awarded by Ocean University of China 2012 Social practice scholarship of OUC Awarded by Ocean University of China 2011 1st prize in National college student mathematical contest in modeling, Shandong area Awarded by Shandong Province, China Non-academic 2015 3rd prize on OUC graduate students mixed-double badminton competition Awarded by Ocean University of China 2014 Excellent student in the 5th graduate student studies of Chinese ancient civilization activity Awarded by Ocean University of China 2013 Excellent student in the 4th graduate student studies of Chinese ancient civilization activity Awarded by Ocean University of China 2013 2nd prize on School of Mathematical Science graduate female students badminton competition Awarded by School of Mathematical Science of Ocean University of China Occupational Skills Languages English Fluent Chinese Native French and German Beginner Abstract The works of this thesis fall into the broad, highly interdisciplinary field of research on opinion dynamics and social networks, which has been studied from different perspectives by sociologists, social psychologists, economists, politicians, cybernetists, mathematicians, computer scientists and even theoretical physicists, for many decades. So far, most models make the basic assumption that agents tend to follow the trend (they are conformist) and that nobody has a kind of opposite behavior (anti-conformism). Recently, a few studies consider such kind of opposite behavior, under the name of anti-conformists, hipsters, contrarians, anti-coordination, etc. Unlike the well-developed theory of opinion dynamics with conformists, the studies with anti-conformists are taking their first steps. This Ph.D thesis aims to answer the following questions: Given a society of agents in a (fixed or endogenous) network, given a mechanism of influence for each agent, how the behavior/opinion of the agents will evolve with time, and in particular can it be expected that it converges to some stable situation, and in this case, which one? The main objective is to obtain the conditions (both on the agent- and network-level) required to generate specific network level phenomena, e.g., reaching a consensus/polarization. The first work provides a detailed study of the threshold model, where both conformist and anti-conformist agents coexist. The study bears essentially on the convergence of the opinion dynamics in the society of agents, i.e., finding absorbing classes, cycles, etc. Also, we are interested in the existence of cascade effects, as this may constitute an undesirable phenomenon