Special Issue in Honor of the 60Th Birthday of Sylvain Sorin

Journal of Dynamics and Games doi:10.3934/jdg.2014.1.3i c American Institute of Mathematical Sciences Volume 1, Number 3, July 2014 pp. i–iv

PREFACE: SPECIAL ISSUE IN HONOR OF THE 60TH BIRTHDAY OF SYLVAIN SORIN

We have the immense pleasure of editing this special issue in honor of Sylvain Sorin.1 It follows the international conference “GameS and StrategY in PariS,” organized by the French school of mathematical game theory, that was also held in his honor. The conference took place at the Institut Henri Poincaré (IHP) in June 2012, included 21 plenary talks and attracted more than 150 participants. After graduating from the Ecole Normale Supérieure (ENS) de Saint Cloud in mathematics in 1976, Sylvain Sorin defended his Thèsed’Etat in 1981 at the Uni- versitéPierre et Marie Curie (UPMC ). He became Professor in 1985—first at the Universitéde Strasbourg (1985-1990) and then at the Universitéde Paris Nanterre (1990-2000)—before joining UPMC in 2000. Concomitantly, he also taught at sev- eral different institutions2 and was a member of the Mathematics Department of the ENS ULM (1990-1995) and of the Laboratoire d’Econometrie´ de l’Ecole Poly- technique (1995-2013). Sylvain was a visiting member of many institutions and universities,3 took on editorial responsibilities as Area Editor of Mathematics of Operations Research and Editor of the International Journal of Game Theory, and was or continues to be an associate editor of many journals in operations research, mathematics and economics.4 He founded the Paris Game Theory Seminar, held at the IHP since 1995, and cofounded the Paris Optimization Seminar held at the IHP since 2004. He has organized, alone or with others, more than 30 summer schools/conferences/workshops. He is one of the founders of the Masters programme Optimisation, Jeux et Modélis- ation en Economie´ in 1995 and was for many years its director. The program has trained many of the young prominent French game theorists in economics, mathematics and computer science. Sylvain has many correspondents and co-authors throughout the world, and has published more that 65 articles in international journals in mathematics, game theory and economic theory that cover many fields, including: repeated games [26, 16, 25, 26, 35], incomplete information and stochastic games [5, 20, 21, 22, 23, 24, 27, 28], dynamic programing [11, 15, 36], market games [29], learning algorithms and game dynamics [8,9, 33, 34], merging and reputation [30], mechanisms [12], approachability [1], congestion games [6, 37], stochastic approximations and dynamical systems

1We thank Michel Balinski, Dinah Rosenberg and Nicolas Vieille for useful comments. 2Ecole Nationale d’Administration (1979), ENS Saint Cloud (1982-1985), Ecole Nationale de la Statistique et de l’Administration Economique´ (1984-1990), and Ecole Polytechnique (2007-2010). 3IMSSS (Stanford), CORE (Louvain), IAS (Jerusalem), MSRI (Berkeley), IDS (Stony Brook), CRIDT (Jerusalem), CMM (Santiago), IMPA (Rio), CRM (Barcelona), HIM (Bonn) and universities: Tel Aviv, Stony Brook, Bielefeld, Vigo, UCL, La Habana, Haifa, Jerusalem, UCLA, Bir-Zeit, Santiago de Chile, Hanoi,... 4RAIRO Operations Research, Annales d’Economie et de Statistiques, Games and Economic Behavior, Journal of Dynamic and Games, Acta Applicandae Mathematicae, Journal of Convex Analysis, Mathematiques et Applications.

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[3,4], bounded rationality [2], maximal monotone operators [7, 19, 32]. He is the author of three books [14, 10, 31] and the editor of two proceedings [13], [17]. In particular, his well-known book [14], with J-F. Mertens and S. Zamir, is extremely deep and comprehensive, and his 2002 book [31] is an excellent introduction to the field of repeated games. Sylvain Sorin likes teaching and presenting. He is an energetic teacher ambi- tious for his students. Past students recall with a delight that replaces the initial trepidation their first course with him: 20 hours for an “Introduction to Game Theory” that covered most of game theory and in which sequential equilibria was mentioned in the first lecture. With his enthusiasm and leading spirit, his strong views on which topics are important and which ones are anecdotic, he has shaped and greatly influenced the French game theory community. He was and still is devoted to his current and past students. He has had, up to now, 21 PhD students5 including 3 current ones, and many of his former students are in academia. He spends a lot of time listening to their ideas, reading the n-th version of their papers (which are invariably returned with many comments, corrections, suggestions, im- provements, new references, open questions, etc). Apart from his students, he has also influenced many others in game theory6. Sylvain likes to solve hard problems neatly, abstractly, to have precise results, to use original ideas to prove them. He is mainly motivated by mathematical generality and the beauty of the statement. He likes game theory because it raises problems simple to state but hard to solve, and since the field is relatively recent, innovation is essential, calling on ideas coming from a large variety of mathematical fields (probability theory, statistics, algebra, analysis, optimization, dynamical systems, . . . ). He likes to talk about his ideas, to share them freely and openly and is delighted when they are adopted. He likes also to find new more insightful proofs of existing results that can be better understood and, in particular, that unify. He is devoted to transmitting and spreading advances in games and dynamics. He devotes a lot of time to understanding and improving other people’s ideas, just for the beauty of it. He is a cultivated mathematician, few researchers read and know the literature as he does. Sylvain likes enumerating the list of participants of his first International Con- ference on Game Theory at Cornell University in 1978. He also likes wine, cigars, cheese, oysters, sun, meat, fish, tennis, piano, music, cognac, photography, expo- sitions, architecture, museums, travels, . . . He also has some dislikes, but that is another story!

REFERENCES

[1] S. Assoulamani, M. Quincampoix and S. Sorin, Repeated games and qualitative diﬀerential games: Approachability and comparison of strategies, SIAM J. on Control and Optimization, 48 (2009), 2461–2479. [2] R. J. Aumann and S. Sorin, Cooperation and bounded recall, Games and Economic Behavior, 1 (1989), 5–39.

5In chronological order, his students were: N. Vieille, J.-M. Coulomb, O. Gossner, P. Goutal, Ph. Riviere, D. Rosenberg, R. Laraki, X. Spinat, J.-P. Beaud, T. Boulogne, Y. Viossat, J. Pey- pouquet, G. Vigeral, V. Perchet, C. Wan, M. Bravo, R. Combes, M. Oliu-Barton, P. Maldonado, X. Li, J. Kwon. 6Such as: J. Bolte, P. Cardaliaguet, M. Faure, F. Gensbittel, B. de Meyer, M. Quincampoix, M. Laclau, J. Renault, G. Stoltz, T. Tomala. PREFACE iii

[3] M. Benaim, J. Hofbauer and S. Sorin, Stochastic approximations and differential inclusions, SIAM J. on Control and Optimization, 44 (2005), 328–348. [4] M. Benaim, J. Hofbauer and S. Sorin, Stochastic approximations and differential inclusions. Part II: Applications, Mathematics of Operations Research, 31 (2006), 673–695. [5] R. Cardaliaguet, R. Laraki and S. Sorin, A continuous time approach for the asymptotic value in two-person zero-sum repeated games, SIAM J. on Control and Optimization, 50 (2012), 1573–1596. [6] R. Cominetti, E. Melo and S. Sorin, A payoff-based learning procedure and its application to traffic games, Games and Economic Behavior, 70 (2010), 71–83. [7] R. Cominetti, J. Peypouquet and S. Sorin, Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization, Journal of Differential Equations, 245 (2008), 3753–3763. [8] J. Hofbauer and S. Sorin, Best response dynamics for continuous zero-sum games, Discrete and Continuous Dynamical Systems Series B, 6 (2006), 215–224. [9] J. Hofbauer, S. Sorin and Y. Viossat, Time average replicator and best reply dynamics, Mathematics of Operations Research, 34 (2009), 263–269. [10] R. Laraki, J. Renault and S. Sorin, Bases Mathématiquesde la Théoriedes Jeux, Editions de l’Ecole Polytechnique, 2013. [11] E. Lehrer and S. Sorin, A uniform tauberian theorem in dynamic programming, Mathematics of Operations Research, 17 (1992), 303–307. [12] E. Lehrer and S. Sorin, One-shot public mediated talk, Games and Economic Behavior, 20 (1997), 131–148. [13] J.-F. Mertens and S. Sorin, Game Theoretic Methods in General Equilibrium Analysis, (NATO ASI), Kluwer Academic Publishers, 1994. [14] J.-F. Mertens, S. Sorin and S. Zamir, Repeated Games, Cambridge University Press, to appear, 2014. [15] D. Monderer and S. Sorin, Asymptotic properties in dynamic programming, International Journal of Game Theory, 22 (1993), 1–11. [16] A. Neyman and S. Sorin, Equilibria in repeated games of incomplete information: The general symmetric case, International Journal of Game Theory, 27 (1998), 201–210. [17] A. Neyman and S. Sorin, Stochastic Games and Applications, (NATO ASI), Kluwer Academic Publishers, 2003. [18] A. Neyman and S. Sorin, Repeated games with public uncertain duration process, Interna- tional Journal of Game Theory, 39 (2010), 29–52. [19] J. Peypouquet and S. Sorin, Evolution equations for maximal monotone operators: Asymp- totic analysis in continuous and discrete time, Journal of Convex Analysis, 17 (2010), 1113– 1163. [20] J.-P. Ponssard and S. Sorin, Optimal behavioral strategies in zero-sum games with almost perfect information, Mathematics of Operations Research, 7 (1982), 14–31. [21] D. Rosenberg and S. Sorin, An operator approach to zero-sum repeated games, Israel Journal of Mathematics, 121 (2000), 221–246. [22] S. Sorin, Some results on the existence of Nash equilibria for non zero-sum games with incomplete information, International Journal of Game Theory, 12 (1983), 193–205. [23] S. Sorin, “Big Match” with lack of information on one side, Part I, International Journal of Game Theory, 13 (1984), 201–255. [24] S. Sorin, “Big Match” with lack of information on one side, Part II, International Journal of Game Theory, 14 (1985), 173–204. [25] S. Sorin, On a repeated game with state dependent signalling matrices, International Journal of Game Theory, 14 (1985), 249–272. [26] S. Sorin, On repeated games with complete information, Mathematics of Operations Research, 11 (1986), 147–160. [27] S. Sorin, Asymptotic properties of a non zero-sum stochastic game, International Journal of Game Theory, 15 (1986), 101–107. [28] S. Sorin, On repeated games without a recursive structure: Existence of lim vn, International Journal of Game Theory, 18 (1989), 45–55. [29] S. Sorin, Strategic market games with exchange rates, Journal of Economic Theory, 69 (1996), 431–446. [30] S. Sorin, Merging, reputation and repeated games with incomplete information, Games and Economic Behavior, 29 (1999), 274–308. iv PREFACE

[31] S. Sorin, A First Course on Zero-Sum Repeated Games, Math´ematiqueset Applications, 37, Springer, 2002. [32] S. Sorin, Asymptotic properties of monotonic non expansive mappings, Discrete Events Dy- namic Systems, 14 (2004), 109–122. [33] S. Sorin, Exponential weight algorithm in continuous time, Mathematical Programming, 116 (2009), 513–528. [34] S. Sorin, On some global and unilateral adaptive dynamics, Evolutionary Game Dynamics (ed. K. Sigmund), Proceedings of Symposia in Applied Mathematics, 69, AMS, 2011, 81–109. [35] S. Sorin and G. Vigeral, Existence of the limit value of two person zero-sum discounted repeated games via comparison theorems, Journal of Optimization Theory and Applications, 157 (2013), 564–576. [36] S. Sorin, G. Vigeral and X. Venel, Asymptotic properties of optimal trajectories in dynamic programming, Sankhya, 72 (2013), 237–245. [37] S. Sorin and C. Wan, Delegation equilibrium payoﬀs in integer-splitting games, RAIRO Op- erations Research, 47 (2013), 47–58.

Guest Editors: Josef Hofbauer, Rida Laraki and J´erˆomeRenault