Research Papers

Book

1. Cardaliaguet P., Delarue F., Lasry J.M., Lions P.L. The master equation and the convergence problem in mean field games. (2019) Princeton University Press (link) (early version arXiv:1509.02505)

Preprints

1. Cannarsa, P., Capuani, R., Cardaliaguet, P. (2018). Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system. arXiv preprint arXiv:1812.11374.

2. Briand, P., Cardaliaguet, P., de Raynal, P. É. C., Hu, Y. (2019). Forward and Backward Stochastic Differential Equations with normal constraint in law. arXiv preprint arXiv:1903.01114.

3. Cardaliaguet, P., Forcadel, N. (2019). From heterogeneous microscopic traffic flow models to macroscopic models. arXiv preprint arXiv:1907.02310.

4. Cardaliaguet, P., Cirant, M., Porretta, A. (2020). Splitting methods and short time existence for the master equations in mean field games. arXiv preprint arXiv:2001.10406.

5. Bardi, M., Cardaliaguet, P. (2020). Convergence of some Mean Field Games systems to aggregation and flocking models. arXiv preprint arXiv:2004.04403.

6. Cardaliaguet, P., Dirr, N., Souganidis, P. E. (2020). Scaling limits and stochastic homogenization for some nonlinear parabolic equations. arXiv preprint arXiv:2004.03857.

Published (or about to be) articles:

1. Cardaliaguet P, Cirant M., Porretta A. Remarks on Nash equilibria in mean field game models with a major player. To appear in Proceedings of the AMS. arXiv preprint arXiv:1811.02811.

2. Cardaliaguet, P., Rainer, C. (2019) An example of multiple mean field limits in ergodic differential games. To appear in SICON. arXiv preprint arXiv:1907.09785.

3. Cardaliaguet, P., Masoero, M. (2019). Weak KAM theory for potential MFG. To appear in Journal of Differential Equations. arXiv preprint arXiv:1904.13287.

4. P. Cardaliaguet, C. Rainer, On the (in)efficiency of MFG equilibria. To appear in SICON. arXiv:1802.06637

5. Cardaliaguet P., Porretta A., Long time behavior of the master equation in mean-field game theory. Analysis and PDEs, Vol. 12 (2019), No. 6, 1397-1453. arXiv:1709.04215

6. Cardaliaguet, P. (2019). On the Convergence of Open Loop Nash Equilibria in Mean Field Games with a Local Coupling. In Trends in Control Theory and Partial Differential Equations (pp. 105-122). Springer, Cham.

7. P. Cannarsa, R. Capuani, P. Cardaliaguet, $C^{1,1}$-smoothness of constrained solutions in the calculus of variations with application to mean field games., Mathematics in Engineering (2018) 1(1), 174-203. arXiv:1806.08966.

8. Cardaliaguet P., Lehalle C.-A. Mean Field Game of Controls and An Application To Trade Crowding. Mathematics and Financial Economics 12 (2018), no 3, 335-363. arXiv:1610.09904

9. Cardaliaguet P., Le Bris C. and Souganidis P.E.. Perturbation problems in homogenization of Hamilton-Jacobi equations. To appear in J. Math. Pures et Appl. ArXiv:1701.05440

10. Briani A., Cardaliaguet P., Stable solutions in potential mean field game systems. NoDEA, 25(1):1, 2018. ArXiv:1612.01877

11. Cardaliaguet P., The convergence problem in mean field games with a local coupling. Appl. Math. Optim. (2017) 76, 177-215. arXiv:1610.06410

12. Cardaliaguet P., Souganidis P. On the existence of correctors for the stochastic homogenization of viscous Hamilton-Jacobi equations. C.R. Acad. Sci. Paris, Ser.I 355 (2017), 786-794, arXiv:1704.07602

13. Armstrong S., Cardaliaguet P. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. To appear in JEMS. ArXiv

14. Cardaliaguet P., Mészaros A.R, Santambrogio F. First order Mean Field Games with density constraints: Pressure equals Price. SIAM J. Control Optim. 54 (2016), no. 5, 2672-2709. Arxiv

15. Cardaliaguet P., Hadikhanloo S. Learning in Mean Field Games: the Fictitious Play. COCV 23 (2017) 569--591. Arxiv

16. Cardaliaguet P, Porretta A., Tonon D., Sobolev regularity for the first order Hamilton-Jacobi equation. Calculus of variation and PDE, (2015) 54. pp. 3037-3065. Arxiv

17. Cardaliaguet P, Graber J., Porretta A., Tonon D., Second order mean field games with degenerate diffusion and local coupling. Nonlinear Differ. Equ. Appl. 22 (2015), 1287-1317. Arxiv

18. P. Cardaliaguet, C. Rainer, D. Rosenberg, N. Vieille, Markov games with frequent actions and incomplete information. To appear in Math. Oper. Res. Arxiv

19. Cardaliaguet P., Graber J., Mean field games systems of first order. ESAIM : COCV 21-3 (2015) 690---722. Arxiv

20. Cardaliaguet P., Souganidis P., Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations. Annales de l'IHP/Analyse Non Linéaire, 32, 3, May-June 2015, Pages 571---591. Arxiv

21. Armstrong S., Cardaliaguet P., Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations. Comm. Partial Differential Equations 40 (2015), no. 3, 540-600. Arxiv

22. P. Cardaliaguet, C. Jimenez, M. Quincampoix, Pure and Random strategies in differential game with incomplete information. J. Dynamic and Games Vol. 1, no. 3 (20014), 363-375

23. Armstrong S., Cardaliaguet P., Souganidis P. Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations. J. American Math. Soc. Vol. 27, N. 2, (2014), 479—540. Arxiv

24. P. Cardaliaguet, J.-M. Lasry, P.-L. Lions, A. Porretta, Long time average of mean field games, with a nonlocal coupling. SIAM J. Control Optim. Vol. 51, No. 5 (2013), pp. 3558—3591.

25. Cardaliaguet P., Long time average of first order mean field games and weak KAM theory. Dyn Games Appl (2013) 3:473—488 Arxiv

26. P. Cardaliaguet, P. E. Souganidis, Homogenization and enhancement for the $G-$equation in random environment. Comm. Pure Applied Math., Vol. 66, N. 10 (2013), 1582--1628. Arxiv

27. Cardaliaguet P., Catherine R. Pathwise strategies for stochastic differential games with an erratum to ''Stochastic Differential Games with Asymmetric Information." Appl. Math. Optim. 68 (2013), no. 1, 75--84.

28. Cardaliaguet P., Silvestre L., Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side. Communications in Partial Differential Equations, vol. 37 (2012), no 9, p. 1668-1688. Arxiv

29. Geodesics for a class of distances in the space of probability measures. (with G. Carlier, B. Nazaret) Calculus of Variations and Partial Differential Equations, (2012) 1-26. Arxiv

30. Long time average of mean field games (with J.-M. Lasry, P.-L. Lions, A. Porretta), Networks and Heterogeneous Media, 7 (2012), 2, 279--301.

31. A differential game with a blind player. (with A. Souquière) Siam J. Control Opti. 50 (2012), 4, 2090—2116. Arxiv

32. Games with incomplete information in continuous time and for continuous types. (with Rainer C.) Dynamic Games and Applications, 2, 2 (2012), 206--227.

33. A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games (with Laraki R., Sorin S.). SIAM Cont. Optimization, 50, 3 (2012), 1573--1596.

34. Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients (with Cannarsa P). NoDEA, 19, 6 (2012), 751—769.

35. Hölder regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton-Jacobi equations with super-quadratic growth in the gradient. (with Rainer C.) SIAM J. Control Optim. 49 (2011), no. 2, 555--573.

36. Some Recent Aspects of Differential Game Theory. (with Buckdahn R., Quincampoix M.) Dyn. Games Appl (2011) 1, 74—114.

37. Optimal transport with convex obstacle.(with Jimenez C.) J. Math. Anal. Appl. 381 (2011), 43—63.

38. Viscosity solutions for a polymer crystal growth model (with O. Ley and A. Monteillet) To appear in Indiana Univ. Math. J.

39. Homogenization and enhancement for the G-equation (with J. Nolen and P. Souganidis) To appear in Arch. Rat. Mec. Anal. 199, 2 (2011), pp. 527-561.

40. Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in $\R^2/\Z^2$. Ann. I. H. Poincaré - AN 27 (2010), 837—856.

41. Hölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equations. (with P. Cannarsa) Communications on Pure and Applied Mathematics 63, 5 (2010), 590-629.

42. A double obstacle problem arising in differential game theory. J. Math. Anal. Appl. 360 (2009), no. 1, 95--107.

43. On a continuous time game with incomplete information. (with C. Rainer) Math. Oper. Res. 34 (2009), no. 4, 769—794.

44. On a differential model for growing sandpiles with non-regular sources. (with P. Cannarsa and C. Sinestrari) Comm. Partial Differential Equations 34 (2009), no. 7-9, 656—675.

45. Numerical approximation and optimal strategies for differential games with lack of information on one side. Advances in dynamic games and their applications, 159--176, Ann. Internat. Soc. Dynam. Games, 10, Birkhäuser Boston, Inc., Boston, MA, 2009.

46. Uniqueness results for non-local Hamilton-Jacobi equations. (with G. Barles, O. Ley and A. Monteillet) J. Functional Anal. 257, 5 (2009), 1261-1287.

47. Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations. (with G. Barles, O. Ley and A. Monteillet) Nonlinear Anal. 71 (2009), no. 7-8, 2801—2810.

48. A discussion about the homogenization of moving interfaces (with P.-L. Lions, P. Souganidis). J. Math. Pures Appl.} (9) 91 (2009), no. 4, 339—363.

49. (pdf) Stochastic differential games with asymmetric information (with C. Rainer). Appl Math Optim (2009) 59: 1-36.

50. (pdf) A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable. To appear in COCV.

51. (pdf) Global existence results and uniqueness for dislocation equations (with G. Barles, O. Ley and R. Monneau). SIAM J. Math. Anal. 40 (2008), no. 1, 44--69.

52. Deterministic differential games under probability knowledge of initial condition. (with M. Quincampoix) Int. Game Theory Rev. 10 (2008), no. 1, 1--16.

53. (pdf)On the energy of a flow arising in shape optimization (with O. Ley). Interfaces and Free Boundaries, 10 (2008), 221–241.

54. (pdf) Differential games with asymmetric information. SIAM J. Control Optim. 46 (2007), no. 3, 816—838.

55. (pdf) Representation formulas for differential games with asymmetric information. J. Optim. Theory Appl. 138 (2008), no. 1, 1--16.

56. (ps)  Non fattening condition for the generalized evolution by mean curvature and applications (with S. Biton and O. Ley). Interfaces Free Bound. 10 (2008), no. 1, 1--14.

57. Regularity of eikonal equation with Neumann boundary conditions in the plane: application to fronts with nonlocal terms (with C. Marchi), SIAM J. Control Optim. 45 (2006), no. 3, 1017--1038

58. (dvi) Zero-sum state constraint differential game: existence of a value for Bolza problem (with P. Bettiol and M. Quincampoix), IJGT, V. 34, N. 3, (2006).

59. Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles.(with P. Cannarsa and E. Giorgieri). Trans. Amer. Math. Soc. 359 (2007), no. 6, 2741-2775.

60. (pdf) On some flows in shape optimization (with O. Ley). Arch. Ration. Mech. Anal. 183 (2007), no. 1, 21--58.

61. (pdf) Existence and uniqueness for dislocation dynamics with nonnegative velocity (with O. Alvarez and R. Monneau). Interfaces Free Bound.7 (2005), no. 4, 415--434.

62. Perimeter estimates for reachable sets of control systems (with P. Cannarsa). J. Convex Anal. 13 (2006), no. 2, 253--267.

63. (pdf) Viscosity solutions of Hele-Shaw moving boundary problem for power-law fluid (with E. Rouy). SIAM J. Math. Anal. 38 (2006), no. 1, 143--165

64. (pdf) A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications (with P. Cannarsa, G. Crasta and E. Giorgieri), Calc. Var. Partial Differential Equations 24 (2005), no. 4, 431--457.

65. (pdfSupremal representation of L-infinity functionals (with F. Prinari),  Appl. Math. Optim. 52 (2005), no. 2, 129--141.

66. (pdf) Nash equilibrium payoffs for nonzero-sum stochastic differential games (with R. Buckdahn and C. Rainer), SIAM J. Control Optim. 43 (2004), no. 2, 624--642.

67. (pdf) Representation of equilibrium solutions to the table problem for growing sandpiles (with P. Cannarsa),  J. Eur. Math. Soc. (JEMS) 6 (2004), no. 4, 435--464.

68. Equilibria and strict equilibria of multivalued maps on noninvariant sets. (with G. Gabor and M. Quincampoix) Ann. Pol. Math. 82, No.1, 19-37 (2003)

69. (dvi) Existence and uniqueness of a Nash equilibrium feedback  for a simple nonzero-sum differential game (with S. Plaskacz), in International J. Game Theory (2003) 32, pp. 33-71.

70. (ps) Some uniqueness results for Bernoulli interior free boundary problems in convex domains (with R. Tahraoui),  Electronic J. Diff. Eq.,Vol. 2002 (2002), No. 102, pp.1-16.

71. Equivalence between rank-one convexity and polyconvexity for isotropic sets of $R^{2\times 2}$ (Parts I and II) (with R. Tahraoui), Nonlinear Analysis, Volume 50, Issue 8, (2002), pp. 1179-1239

72. (ps) On the strict concavity of the harmonic radius in dimension N2 (with R. Tahraoui), J.Math. Pures Appl.., 81 (2002) pp. 223-240.

73. A representation formula for the mean curvature motion (with R. Buckdahn and M. Quincampoix), in SIAM J. Math. Anal." (2002), V. 33, N. 4, pp. 827-846.

74. On front propagation problems with non local terms (Part II). in  J. Math. Anal. Appl. '' 260 (2001), pp. 572-601.

75. On the approximation of front propagation problems with non local terms. (with D. Pasquignon) in  RAIRO Mathematical Modeling and Numerical Analysis '' Vol. 35, N. 3 (2001), pp. 437-462.

76. Pursuit differential games with state constraints. (with M. Quincampoix and P. Saint-Pierre) in  SIAM J. Control and Optimization '' Vol. 39, N. 5 (2001),  pp. 1615-1632.

77. (ps) Extended Hardy-Littlewood inequalities and applications to the calculus of variations. (with R. Tahraoui) in  Advances Diff. Eq.'' Volume 5, No. 7-9 (2000) pp: 1091-1138.

78. Radon-Nikodym theorem in $L^\infty$. (with E.N. Barron and R.R. Jensen) in  Appl. Math. Opti.'' Volume 42, No 2 (2000) pp: 103-126.

79. Numerical schemes for discontinuous value functions of optimal control (with M. Quincampoix and P. Saint-Pierre) in  Set-valued Analysis '' Vol. 8, N. 1 & 2 (2000) pp: 111-126.

80. Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable hamiltonians. (with S. Plaskacz) in  SIAM J. Control and Optimization '' Vol. 38, N.5 (2000) pp: 1501-1520.

81. (ps) On front propagation problems with non local terms. in  Advances Diff. Eq.'' Vol. 5, N. 1-3, (2000) pp:213-268.

82. Geometric restriction for the existence of viscosity solutions. (with B. Dacorogna, W. Gangbo and N. Georgy) in  Annales de l'I.H.P., Anal. Non Lineaire '' Vol. 6, N. 2 (1999) pp: 189-220.

83. Numerical methods for differential games. (with M. Quincampoix and P. Saint-Pierre) in  Stochastic and differential games : Theory and numerical methods '' (1999) pp. 177-247. Annals of the international Society of Dynamic Games, M. Bardi, T.E.S. Raghavan, T. Parthasarathy Eds. Birkh\"{a}user.

84. Optimal times for constrained nonlinear control problems without local controllability. (with M. Quincampoix and P. Saint-Pierre) in  Appl. Math. Opti.'' Vol. 36 (1997) pp: 21-42.

85. On the regularity of Semi-Permeable Surfaces in Control Theory with application to the optimal exit-time problem (Part I and II) in  SIAM J. Control and Optimization '' Vol. 35, N. 5 (1997) pp: 1638-1671.

86. Nonsmooth semi-permeable barriers, Isaacs' equation, and application to a differential game with one
target and two players, in  Appl. Math. Opti.",  36, 125-146.

87. A differential game with two players and one target SIAM J. Control and Optimization", Vol. 34, N. 4 (1996)
pp. 1441-1460.

88. Some Algorithms for Differential Games with two Players and one Target (with M. Quincampoix and P. Saint-Pierre), in  RAIRO Mathematical Modeling and Numerical Analysis '', Vol. 28, N. 4,  pp. 441-461.

Last update: 2019/06/15