14The 17th International Symposium on Dynamic Games and Applications
July 12-15, 2016 Urbino, Italy Preliminary Program
Program Overview Tuesday, July 12 8:00 - 8 :30
Registration
8:30 - 8 :45
Opening Address
8:45 - 9:45
Plenary I: H. Kokko
9:45 - 10:15
Coffee Break
10:15 - 12:15
Parallel Sessions TA Mean Field Games and their applications I Cooperative Differential Games Dynamic Games in Economics and Finance I Dynamic Games in Environmental Economics I
12:30 - 14:15
Lunch
14:15 - 16:15
Parallel Sessions TB Mean Field Games and their applications II Game theory in networks I Evolutionary Games I Dynamic Games in Management I
16:15 - 16:45
Coffee Break
16:45 - 18:15
Parallel Sessions TC Dynamic Games Evolutionary Games and Complex Systems I Dynamic Games in Economics and Finance II Differential games I
19:30
Welcome Party
Aula magna Conference Hall Aula magna Conference Hall
University canteen “Mensa del Duca”
Basili’s
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Wednesday, July 13 8:30 - 10:00
Parallel Sessions WA Dynamic Games in Economics and Finance III Differential games II Game theory in networks II Numerical methods
10:00 - 10:30
Coffee Break
10:30 - 12:30
Parallel Sessions WB Differential games III Evolutionary Games II Dynamic Games in Environmental Economics II Mean Field Games and their applications III
12:45 - 14:15
Lunch
14:15 - 16:15
Parallel Sessions WC Evolutionary Games III Dynamic Games in Environmental Economics III Mean Field Games and their applications IV Pursuit-evasion games
16:15 - 16:45
Coffee Break
16:45 - 18:15
Parallel Sessions WD Evolutionary Games and Complex Systems II Dynamic Games in Economics and Finance IV Dynamic Games in Environmental Economics IV Mean Field Games and their applications V
University canteen “Mensa del Duca”
Thursday, July 14 8:30 - 10 :00
Tutorial I (Part 1): A. Nedich
10:00 - 10:30
Coffee Break
10:30 - 12:00
Tutorial I (Part 2): A. Nedich
12:00 - 12:30
General Assembly of ISDG
12:45 - 14:15
Lunch
14:15 - 15:15
Plenary II: R. Cellini
15:15 19:30 -
Visit to Palazzo Ducale Social Dinner
Aula magna Conference Hall Aula magna Conference Hall Aula magna Conference Hall University canteen “Mensa del Duca” Aula magna Conference Hall Univ. restaurant “Il Colle” 4
Friday, July 15 8:00 - 9:30
Tutorial II (Part 1): P. Cardaliaguet
9:30 - 10:00
Coffee Break
10:00 - 11:25
Tutorial II (Part 2): P. Cardaliaguet
11:25 – 11:40
Break
11:40 - 13:00
Isaacs Awards Presentations
13:00 - 14:30
Lunch
14:30 - 16:30
Parallel Sessions FA Mean Field Games and their applications VI Dynamic Games in Management II Stochastic games Game theory in networks III
16:30 - 16:40
Break
16:40 - 17:00
Closing
Aula magna Conference Hall Aula magna Conference Hall Aula magna Conference Hall University canteen “Mensa del Duca”
Aula magna Conference Hall
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Tuesday, July 12 8:00 – 8:30
Registration
8:30 – 8:45
Opening Address
8:45 – 9:45
Plenary I. Chair: Joseph Apaloo Dynamic consequences of the fact that populations often have two sexes Hanna Kokko, University of Zurich, Switzerland
9:45 – 10:15
Coffee Break
Aula Magna
10:15 – 12:15 PARALLEL SESSIONS TA TA1
Mean Field Games and their applications I. Chair: Elisabetta Carlini
Aula Magna
Mean field competitive Markov decision processes: monotone costs and threshold policies Minyi Huang A Mean-Field Game of Evacuation in a Multi Level Building Boualem Djehiche, Alain Tcheukam, Hamidou Tembine Some results on focusing Mean-Field Games Marco Cirant A Semi-Lagrangian scheme for the Fokker-Planck equation Elisabetta Carlini, A. Festa, F.J Silva, M.T. Wolfram TA2
Cooperative Differential Games. Chair: Leon Petrosyan
Aula Rossa
Strong Time-consistent Core Applicable to Cooperative Resource Extraction Artem Sedakov, Han Qiao, Shouyang Wang A Friendly Computable Characteristic Function Puduru V. Reddy, Georges Zaccour Dynamic Shapley Value for 2-stage cost sharing game with perishable products Yin Li New Strongly Time-Consistent Solutions in Cooperative Differential Games Leon Petrosyan TA3
Dynamic Games in Economics and Finance I. Chair: Nick Huberts
Aula Amaranto
Risk, trust, and cooperation in urban development: Experimental evidence from Belgium, Norway, and the Netherlands Anders Eika, Perrine Dethier, Keyang Li, John Farrel
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Debt Stabilization in a Dynamic Nash Game between a Financial and a Monetary Player in presence of Risk Premia Jacob Engwerda, Janis Anevlavis, Bas van Aarle, George Papavassilopoulos A Non-cooperative Approach to Dynamic Bargaining Francesca Flamini Optimal timing of technology adoption by incumbents: war of attrition versus preemption Nick F.D. Huberts TA4
Dynamic Games in Environmental Economics I. Chair: D. De Giovanni
Aula A1
Tipping Points and Business-as-Usual in a Global Carbon Commons Rodrigo Harrison, Roger Lagunoff Verification and refinement of Fischer-Mirman Fish Wars Model Agnieszka Wiszniewska-Matyszkiel, Oskar Gorniewicz Multi-level Interaction Games in Adaptive Climate Governance Jürgen Scheffran Imperfect control in a managed fishery game Domenico De Giovanni, Fabio Lamantia 12:30 – 14:15 Lunch
Mensa del Duca
14:15 – 16:15 PARALLEL SESSIONS TB TB1
Mean Field Games and their applications II. Chair: Dario Bauso
Aula Magna
Pressure and resistance in evolutionary and mean-field game framework Vassili Kolokoltsov Random Entrance and Duration of Overlapping Generation Games: Impact on Stability and Gains Ioannis Kordonis, George Papavassilopoulos Aggregative game theoretic control of large populations of plug-in electric vehicles Sergio Grammatico Dynamic demand via mean-field games Dario Bauso TB2
Game theory in networks I. Chair: Tania Jiménez
Aula Rossa
Caching strategically in 5G networks Francesco De Pellegrini, Antonio Massaro, Antonio Goratti, Rachid El Azouzi A Double Auction Mechanism for Smart-Grids with flexible Consumers Corinne Touati, Angan Mitra, Stéphane Ploix 7
Modeling Autoregulation of Cerebral Blood Flow using Viability Approach Varvara L. Turova, Nikolai D. Botkin, Ana Alves-Pinto, Tobias Blumenstein, Esther RiegerFackeldey, Renée Lampe Road Traffic Games with Environmental Issues Yezekael Hayel, Tania Jiménez TB3
Evolutionary Games I. Chair: Katerina Stankova
Aula Amaranto
Evolutionary stability of polymorphic states in continuous games K.S. Mallikarjuna Rao Evolutionary Behavior of Taxpayers in the Model of Information Spreading Elena A. Gubar, Ekaterina M. Zhitkova, Suryia Sh. Kumacheva The Interplay of Identity and Social Network: An Evolutionary Game Model Abhishek Ray, Ghatak Anirban, Mukherjee Diganta Games of cancer Katerina Stankova TB4
Dynamic Games in Management I. Chair: Guiomar Martin-Herran
Aula A1
A Dynamic CLSC Game with Price and Technology Dependent Returns Talat Genc, Pietro De Giovanni Enhancing Environmental Reputation through Process Innovation Investments and Cooperative Programs Pietro De Giovanni, Liu Baolong Optimal dynamic advertising under time inconsistent preferences Lijue Lu, Jorge Navas Divisible good uniform price auction with asymmetric bidders and non-monotonic evaluation functions Odile Pourtallier, Mabel Tidball 16:15 – 16:45 Coffee Break 16:45 – 18:15 PARALLEL SESSIONS TC TC1
Dynamic Games. Chair: Nikolai Botkin
Aula Magna
Backgammon as dynamic game Sergei Dotsenko Robust and optimistic games with bounded polyhedral uncertainty sets Giovanni Paolo Crespi, Davide Radi, Matteo Rocca 8
Viability Approach to Aircraft Control in Windshear Conditions Nikolai D. Botkin, Johannes Diepolder, Varvara L. Turova, Matthias Bittner, Florian Holzapfel TC2
Evolutionary Games and Complex Systems I. Chair: Elena Gubar
Aula Rossa
How to derive static fitness optimization criteria from replicator dynamics models? Case of sex ratio and nest site lottery models. Krzysztof Argasinski Evolution of ecological food web networks Rosalyn Rael Impulse Vaccination in Evolutionary Epidemic Model with Virus Mutation Elena Gubar, Quanyan Zhu, Vladislav Tainitskiy TC3
Dynamic Games in Economics and Finance II. Chair: Luca Grilli
Aula Amaranto
Delaying Product Innovation in Duopoly: A Dynamic Analysis with Endogenous Time Horizon Herbert Dawid, Serhat Gezer Modelling the interaction between a flooding event and firms profit maximization using impulse control theory Johanna Grames, Peter Kort, Dieter Grass, Alexia Prskawetz A Duopoly Model with Common Renewable Public Resource and Incentives in Finite Time Horizon Luca Grilli, Michele Bisceglia TC4
Differential Games I. Chair: Gustav Feichtinger
Aula A1
Uniform Tauberian Theorem for value functions Dimitrii Khlopin LQG Dynamic Games Meir Pachter Buying a Stairway to Heaven: A Strategic Approach Towards Love Dynamics Gustav Feichtinger, Jonathan P. Caulkins, Andrea Seidl 19:30
Welcome Party
Basili’s
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Wednesday, July 13 8:30 – 10:00 PARALLEL SESSIONS WA WA1 Dynamic Games in Economics and Finance III. Chair: Fabio Lamantia
Aula Magna
Dynamic tax competition: a differential game approach Simon Hoof Technological Innovation, Human Capital and Income Distribution: An Evolutionary MacroDynamic Model Julia Mendonca da Costa, Edgar J. Sanchez Carrera Strategic Delegation in Evolutionary oligopoly with nonlinear demand Domenico De Giovanni, Fabio Lamantia WA2 Differential games II. Chair: Anna Rettieva
Aula Rossa
Analytic solutions for a class of HJB equations Arsen Palestini Lion and Man Game in Compact Spaces Olga Yufereva Equilibria in dynamic multicriteria games with incomplete information Anna Rettieva WA3 Game theory in networks II. Chair: Eitan Altman
Aula Amaranto
Anti-crowding game for individual protection against virus in general network Francois-Xavier Legenvre, Y. Hayel and Eitan Altman Wardrop equilibria and relaxation oscillations in queuing systems Vivek Borkar, Corinne Touati A sequential game model for analysing network non-neutrality Eitan Altman WA4 Numerical methods. Chair: Rajani Singh
Aula A1
Upper convex hulls method for solving differential games with non-terminal payoff Mikhail Gomoyunov Parallel Computing of the Viability Kernel Sthéphane Le Ménec Numerical versus analytic calculation of optima and equilibria in Fish Wars model with finite time horizon Rajani Singh, Agnieszka Wiszniewska-Matyszkiel 10
10:00 – 10:30 Coffee Break 10:30 – 12:30 PARALLEL SESSIONS WB WB1 Differential games III. Chair: Dean Carlson
Aula Magna
Cooperation in Time Dependent Transportation Networks Victor V. Zakharov Set-valued mappings and their selections in dynamic game problems Viktoria Chikriy The effect of impunity in behavior corruptible agent Lucas Nascimento, Rodrigo Calmon Ribeiro Open-loop Nash Equilibria for Dynamic Games involving Volterra Integral Equations Dean Carlson WB2 Evolutionary Games II. Chair: Chaitanya Gokhale
Aula Rossa
Neighbourhood Invader Strategy: A Review Joseph Apaloo Evolutionary game theory under time constraint Ross Cressman Evolutionary dynamics and the resolution of natural selection Yosef Cohen Ecological dynamics in evolutionary games Chaitanya S. Gokhale WB3 Dynamic Games in Environmental Economics II. Chair: Alain Jean-Marie
A. Amaranto
Does environmental connotation affect coordination issues in an experimental stag hunt game? Mabel Tidball, Dimitri Dubois, Stefano Farolfi, Mathieu Désolé, Annie Hofstetter Spatial effects in a multiregional transboundary pollution game: Cooperative and Noncooperative strategies Javier de Frutos, Guiomar Martín-Herrán The evolutionary lake game Michael Finus, Paolo Zeppini, Aart de Zeeuw Extraction cost: before or after harvesting? Economic and environmental consequences. Alain Jean-Marie, Mabel Tidball
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WB4 Mean Field Games and their applications III. Chair: Martino Bardi
Aula A1
Mean field games with absorption Markus Fischer, Luciano Campi Non-memoryless pedestrian flow in a crowded environment with target sets Fabio Bagagiolo, Raffaele Pesenti Decentralized routing problem via mean-field game. Rosario Maggistro, Bagagiolo Fabio, Dario Bauso New results on Mean-Field Games with several populations of agents Yves Achdou, Martino Bardi, Marco Cirant 12:45 – 14:15 Lunch
Mensa del Duca
14:15 – 16:15 PARALLEL SESSIONS WC WC1
Evolutionary Games III. Chair: Vlastimil Krivan
Aula Magna
Understanding the occurrence of cry-wolf plants in a tri-trophic system Katerina Stankova The world’s biomes and primary production as a triple tragedy of the commons foraging game played among plants Gordon G. McNickle, Miquel A. Gonzalez-Meler, Douglas J. Lynch, Jennifer L Baltzer, Joel S. Brown Instability of Simple Decision Schemes Dashiell Fryer Migration as a game theoretic concept Vlastimil Krivan WC2
Dynamic Games in Environmental Economics III. Chair: Florian Wagener
A. Rossa
On the joint management of a common property resource game with heterogeneous players in a stochastic setting J. Marin-Solano, Anna Castaner, Carmen Ribas The Strategic Use of Abatement to Influence Environmental Policy with a Stock Pollutant Santiago J. Rubio, Guiomar Martín-Herrán Nonlinear differential games with Skiba points Larry Karp, Charles Séguin Unconditional aid and green growth Florian Wagener
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WC3
Mean Field Games and their applications IV. Chair: Roland Malhamé
A. Amaranto
Evolutionary Inspection (Corruption) Game Stamatios Katsikas, Vassili Kolokoltsov Distributed computation of generalized Nash equilibria in aggregative games with coupling constraints Basilio Gentile, Francesca Parise, Dario Paccagnan, Maryam Kamgarpour, John Lygeros Network aggregative games: Distributed control and opinion dynamics Francesca Parise, Basilio Gentile, Sergio Grammatico, John Lygeros Mean Field Based Collective Homing Problems Rabih Salhab, Roland Malhamé, Jérome Le Ny WC4
Pursuit-evasion games. Chair: Valerii Patsko
Aula A1
Attacker-Target-Defender Differential Game in the Simplest Formulation: Numerical Investigation Sergey S. Kumkov, Valerii S. Patsko Coincidence of generalized solution and value function of time-optimal differential game with life line Nataly V. Munts, Sergey S. Kumkov An algorithm of explicit one-step construction of $t$-sections of the maximal stable bridge in games with simple motions in the plane Liudmila Kamneva, Valerii Patsko Pursuit problem with two pursuers and one evader: constructing feedback strategies on the basis of switching lines Sergey S. Kumkov, Valerii S. Patsko, Stéphane Le Ménec 16:15 – 16:45 Coffee Break 16:45 – 18:15 PARALLEL SESSIONS WD WD1 Evolutionary Games and Complex Systems II. Chair: David Ramsey
Aula Magna
Nash and Stackelberg Games for Epidemic Networks with Multiple Viruses Ji Liu, Tamer Başar Evolutionary Games and Poverty Traps Edgar J. Sánchez Carrera On a Large Population Mate Choice Game with Continuous Time David Ramsey
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WD2 Dynamic Games in Economics and Finance IV. Chair: Vladimir Petkov
Aula Rossa
Rent-seeking and Bargaining Haruo Imai Environmental compliance in a world of Quixotes and Sanchos Francisco Cabo, Ana Garcia Gonzalez True Hyperbolic Discounting: Implications for Consumption and Government Policy Vladimir Petkov WD3 Dynamic Games in Environmental Economics IV. Chair: Michèle Breton
A. Amaranto
Groundwater extraction and social networks Jorge Marco, Renan-Ulrich Goetz Non-constant discounting and pollution abatement in an endogenous growth model Francisco Cabo, Guiomar Martín-Herrán, Maria Pilar Martinez-Garcia Mergers in exhaustible resource industries Hassan Benchekroun, Michèle Breton, Amrita Ray Chaudhuri WD4 Mean Field Games and their applications V. Chair: Alain Haurie
Aula A1
Deterministic limit of mean field games associated with nonlinear Markov processes Yurii Averboukh Deriving a Mean Field Games based on Parrondo's Paradox Gershon Wolfe A Mean Field Game Model of Climate Change Mitigation Olivier Bahn, Alain Haurie, Roland Malhamé
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Thursday, July 14 8:30 – 10:00 Tutorial I (Part 1), Chair: Georges Zaccour
Aula Magna
Continuous games: Dynamics and Nash equilibria Angelia Nedich, University of Illinois at Urbana-Champaign, USA 10:00 – 10:30 Coffee Break 10:30 – 12:00 Tutorial I (Part 2), Chair: Georges Zaccour
Aula Magna
Continuous games: Dynamics and Nash equilibria Angelia Nedich, University of Illinois at Urbana-Champaign, USA 12:00 – 12:30 General Assembly of ISDG 12:45 – 14:15 Lunch 14:15 – 15:15 Plenary II. Chair: Bruno Viscolani
Aula Magna Mensa del Duca Aula Magna
Differential games in markets for health Roberto Cellini, University of Catania, Italy 15:15
Visit to Palazzo Ducale
19:30
Social Dinner
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Friday, July 15 8:00 – 9:30
Tutorial II (Part 1), Chair: Roland Malhamé
Aula Magna
Survey on mean field games Pierre Cardaliaguet, Université Paris Dauphine, France 9:30 – 10:00 Coffee Break 10:00 – 11:25 Tutorial II (Part 2), Chair: Roland Malhamé
Aula Magna
Survey on mean field games Pierre Cardaliaguet, Université Paris Dauphine, France 11:25 – 11:40 Break 11:40 – 13:00 Isaacs Awards Presentations 13:00 – 14:30 Lunch
Aula Magna Mensa del Duca
14:30 – 16:30 PARALLEL SESSIONS FA FA1
Mean Field Games and their applications VI. Chair: Astrid Hilbert
Aula Magna
Linear-quadratic mean field teams with mixed players Minyi Huang, Son L. Nguyen The Execution Problem in Finance: A Mean Field Game Formulation Dena Firoozi, Peter E. Caines Methods of the McKean-Vlasov SPDEs for the Mean Field Games with Common Noise Vassili N.Kolokoltsov, Marianna Troeva An approximate Nash Equilibrium for Non-linear Markov Games of Pure Jump Type Astrid Hilbert FA2
Dynamic Games in Management II. Chair: Alessandra Buratto
Aula Rossa
Strategic Interactions between Pharmaceutical Firms and Health Authorities. The Treatment of Expensive Infectious Diseases Andrea Di Liddo Endogenous leadership and market inefficiency in a differential game of R&D Anton Bondarev Dynamics in Research Joint Ventures and R&D Collaborations Mario Samano, Marc Santugini, Georges Zaccour Differential game with a non differentiable point for a sport licensing contract Alessandra Buratto 16
FA3
Stochastic games. Chair: Anna Jaskiewicz
Aula Amaranto
Nash Equilibria in Reactive Strategies Artem Bakhlanov Stationary Anonymous Sequential Games on General Metric Spaces Piotr Więcek Mean Field Game Theory: The Case of Agents with Partial Observations on their Individual States Nevroz Sen and Peter E. Caines Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games Anna Jaskiewicz, Andrzej Nowak FA4
Game theory in networks III. Chair: Vivek Borkar
Aula A1
Compartmentalized Network Dynamics and Price Identity Arnaud Dragicevic Game-Theoretic Centrality Measures for Community Detection in Collaboration Networks Vladimir Mazalov A stopping game with unbounded random horizon Marek Skarupski, Krzysztof Szajowski An ergodic Stackelberg team problem for controlled diffusions Vivek Borkar 16:30 – 16:40 Break 16:40 – 17:00 Closing
Aula Magna
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Presenter Altman, Eitan Apaloo, Joseph Argasinski, Krzysztof Averboukh, Yurii Bagagiolo, Fabio Baklanov, Artem Bardi, Martino Basar, Tamer Bauso, Dario Bondarev, Anton Borkar, Vivek Botkin, Nikolai Breton, Michèle Buratto, Alessandra Cabo, Francisco Caines, Peter Caines, Peter Cardaliaguet, Pierre Carlini, Elisabetta Carlson, Dean Cellini, Roberto Chikriy, Viktoria Cirant, Marco Cohen, Yosef Cressman, Ross de Frutos, Javier De Giovanni, Domenico De Giovanni, Pietro De Pellegrini, Francesco Di Liddo, Andrea Dotsenko, Sergei Dragicevic, Arnaud Eika, Anders Engwerda, Jacob Feichtinger, Gustav Fischer, Markus Flamini, Francesca Fryer, Dashiell Genc, Talat Gezer, Serhat Gokhale, Chaitanya Gomoyunov, Mikhail Gonçalves do Nascimento, Lucas Grames, Johanna Grammatico, Sergio Grilli, Luca
Session WA3 WB2 TC2 WD4 WB4 FA3 WB4 WD1 TB1 FA2 FA4 TC1 WD3 FA2 WD2 FA1 FA3 TU2 TA1 WB1 PL2 WB1 TA1 WB2 WB2 WB3 TA4 TB4 TB2 FA2 TC1 FA4 TA3 TA3 TC4 WB4 TA3 WC1 TB4 TC3 WB2 WA4 WB1 TC3 TB1 TC3
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
Gubar, Elena Gubar, Elena Harrison, Rodrigo Haurie, Alain Hilbert, Astrid Hoof, Simon Huang , Minyi Huang , Minyi Huberts, Nick Imai, Haruo Jaskiewicz, Anna Jean-Marie, Alain Jimenez, Tania Kamneva, Liudmila Katsikas, Stamatios Khlopin, Dmitrii Kokko, Hanna Kolokoltsov, Vassili Kordonis, Ioannis Krivan, Vlastimil Kumkov, Sergey Lamantia, Fabio Le Ménec, Stéphane Legenvre, François-Xavier Li, Yin Maggistro, Rosario Malhamé, Roland Marco, Jorge Marin-Solano, Jesus Martinez-García, María Pilar Mazalov, Vladimir McNickle, Gordon Munts, Nataly Navas, Jorge Nedich, Angelia Paccagnan, Dario Pachter, Meir Palestini, Arsen Parise, Francesca Patsko, Valerii Petkov, Vladimir Petrosyan, Leon Pourtallier, Odile Radi, Davide Rael, Rosalyn Ramsey, David Rao, K.S. Mallikarjuna
TB3 TC2 TA4 WD4 FA1 WA1 TA1 FA1 TA3 WD2 FA3 WB3 TB2 WC4 WC3 TC4 PL1 TB1 TB1 WC1 WC4 WA1 WA4 WA3 TA2 WB4 WC3 WD3 WC2 WD3 FA4 WC1 WC4 TB4 TU1 WC3 TC4 WA2 WC3 WC4 WD2 TA2 TB4 TC1 TC2 WD1 TB3
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94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
Ray, Abhishek Rettieva, Anna Rubio, Santiago J. Sanchez Carrera, Edgar Sanchez Carrera, Edgar Scheffran, Jürgen Sedakov, Artem Séguin, Charles Singh, Rajani Stankova, Katerina Stankova, Katerina Szajowski, Krzysztof Tembine, Hamidou Tidball, Mabel Touati, Corinne Touati, Corinne Troeva, Marianna Turova, Varvara Wagener, Florian Wiecek, Piotr Wiszniewska-Matyszkiel, Agnieszka Wolfe, Gershon Yufereva, Olga Zaccour, Georges Zaccour, Georges Zakharov, Victor Zeppini, Paolo
TB3 WA2 WC2 WA1 WD1 TA4 TA2 WC2 WA4 TB3 WC1 FA4 TA1 WB3 TB2 WA3 FA1 TB2 WC2 FA3 TA4 WD4 WA2 TA2 FA2 WB1 WB3
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