Pierre BERNHARD

Emeritus senior scientist
Project COMORE
INRIA-Sophia Antipolis-Méditerranée

Pierre.Bernhard@sophia.inria.fr

Tel : +33 (0)4 97 15 53 87

Officier de l’ordre national du mérite
Chevalier de la Légion d’Honneur
Prix Michel Monpetit de l’Académie des Sciences

I used to be ...

- Professor (Control theory) at École Nationale Supérieure des Mines de Paris (ENSMP), 1970 – 1976
- Professor (Mathematics) at University Paris 9 Dauphine, 1976 – 1981
- Director of Centre d’Automatique et Informatique, ENSMP, 1972 – 1981
- Director, INRIA-Sophia Antipolis, 1981 – 1996
- Professor (Mathematics) at the university of Nice-Sophia Antipolis (UNS) 1996 – 2009
- Director of I3S, joint laboratory of UNS and CNRS, 2000 – 2004





My research interests ...

are all more or less related to dynamic games and their applications, yesteryear in combat analysis, robust and H-infinity-optimal control, finance and economics, nowadays mainly in mathematical biology: behavioural ecology, evolutionary games, population dynamics.

I am proud to have been awarded the Isaacs Award of the International Society of Dynamic Games, in 2008.

Recent publications

[1] Pierre Bernhard. A robust control approach to option pricing including transaction costs. Annals of the ISDG, 7:391–416, 2005.

[2] Arik Melikyan and Pierre Bernhard. Geometry of optimal trajectories around a focal singular surface in differential games. Applied Mathematics and Optimization, 52:23–37, 2005.

[3] Pierre Bernhard. Chain differentials with an application to the mathematical fear operator. Nonlinear Analysis, 62:1225–1233, 2005.

[4] Pierre Bernhard. The robust control approach to option pricing and interval models: an overview. In Michèle Breton and Hatem Ben-Ameur, editors, Numerical Methods in Finance, pages 91–108. Springer, New York, 2005.

[5] Éric Wajnberg, Pierre Bernhard, Frédéric Hamelin, and Guy Boivin. Optimal patch time allocation for time limited foragers. Behavioural Ecology and Sociobiology, 60:1–10, 2005.

[6] Pierre Bernhard and Anikal J. Shaiju. Evolutionary stable strategies and dynamics: Tutorial, example and open problems. In Guiomar Martin-Herran and Georges Zaccour, editors, 5th ISDG Workshop, Segovia, Spain, September 21–24, 2005, 2005.

[7] A.J. Shaiju and Pierre Bernhard. Evolutionarily stable strategies: Two nontrivial examples and a theorem. In International Symposium on Dynamic Games and Applications, number 12, Sophia Antipolis, France, 2006.

[8] Éric Wajnberg, Frédéric Hamelin, Pierre Bernhard, and Guy Boivin. Durée optimale de l’exploitation des agrégats d’hôtes par des insectes parasitoïdes à durée de vie limitée : approche théorique et vérification expérimentale. In 134`eme r´eunion de la Soci´et´e d’Entomologie du Qu´ebec, Montréal, Canada. 2008.

[9] Eitan Altman, Pierre Bernhard, Merouane Debbah, and Alonso Silva. Contiunum equilibria for routing in dense ad-hoc networks. In Allerton Conference on Communication, Control, and Computing, number 45, Allerton House, Monticello, Il., USA, 2007.

[10] Pierre Bernhard, Stéphane Thiery, and Marc Deschamps. La tarification d’options. proposition pour une approche déterministe.In Congrès annuel de l’Association Française des Sciences Economiques, number 56, Paris, 2007.

[11] Pierre Bernhard, Na¨ıma El Farouq, and St´ephane Thiery. Robust control approach to option pricing: representation theorem and fast algorithm. SIAM Journal on Control and Optimization, 46:2280–2302, 2007.

[12] Frédéric Hamelin, Pierre Bernhard, A.J. Shaiju, and Eric Wajnberg. Diet selection as a differential foraging game. SIAM journal on Control and Optimization, 46:1539–1561, 2007.

[13] Frédéric Hamelin, Pierre Bernhard, and Éric Wajnberg. Superparasitism as a differential game. Theoretical Population Biology, 72:366–378, 2007.

[14] Bernard Roitberg and Pierre Bernhard. State dependent problems for parasitoids: case studies and solutions. In Eric Wajnberg, Carlos Bernstein, and Jacques van Alphen, editors, Behavioural Ecology of Insect Parasitoids. Blackwell, 2007.

[15] Frédéric Hamelin, Pierre Bernhard, Philippe Nain, and Éric Wajnberg. Foraging under competition: evolutionarily stable patch-leaving strategies with random arrival times. 1. scramble competition. In Thomas Vincent, editor, Advances in Dynamic Game Theory, volume 9 of Annals of the ISDG, pages 327–348. 2007.

[16] Frédéric Hamelin, Pierre Bernhard, A.J. Shaiju, and Éric Wajnberg. Foraging under competition: evolutionarily stable patch-leaving strategies with random arrival times. 2 interference competition. In Thomas Vincent, editor, Advances in Dynamic Game Theory, volume 9 of Annals of the ISDG, pages 349–365. 2007.

[17] Andrei Akhmetzhanov, Pierre Bernhard, Frédéric Grognard, and Ludovic Mailleret. Reproduction dynamics in a differential game between foraging predators and hiding preys. In International Symposium on the theory and applications of dynamic games, number 13, Wroclaw, Poland, 2008.

[18] Pierre Bernhard. Ess, population games, replicator dynamics: dynamics and games if not dynamic games. In International Symposium on the theory and applications of dynamic games, number 13, 2008.

[19] Pierre Bernhard and Frédéric Hamelin. Two-by-two static, evolutionary, and dynamic games. In Yves Bertot, Gérard Huet, Jean-Jacques Lévy and Gordon Plotkin, editors, From Semantics to Computer Science: Essays in Honor of Gilles Kahn, pages 452–474. Cambridge University Press, 2008.

[20] Frédéric Hamelin and Pierre Bernhard. Uncoupling Isaacs equations in two-player nonzero-sum differential games. Conflict over parental care as an example. Automatica, 44:882–885, 2008.

[21] Pierre Bernhard, Vladimir Gaitsgory, and Odile Pourtallier. Advances in Dynamic Games and their Applications: Analytical and Numerical Developments, volume 10. Sringer/Birkhäuser, Boston, 2009.

[22] Andrei Akhmetzhanov, Pierre Bernhard, Frédéric Grognard, and Ludovic Mailleret. Competition between foraging predators and a hiding preys as a nonzero-sum differential game. In Gamenets 2009, Istanbul, Turkey, 2009.