**Research Papers**

Book

*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

*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.**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.**Cardaliaguet, P., Forcadel, N. (2019). From heterogeneous microscopic traffic flow models to macroscopic models. arXiv preprint arXiv:1907.02310.**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.**Bardi, M., Cardaliaguet, P. (2020). Convergence of some Mean Field Games systems to aggregation and flocking models. arXiv preprint arXiv:2004.04403.**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:

*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.**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.**Cardaliaguet, P., Masoero, M. (2019). Weak KAM theory for potential MFG. To appear in Journal of Differential Equations. arXiv preprint arXiv:1904.13287.**P. Cardaliaguet, C. Rainer, On the (in)efficiency of MFG equilibria. To appear in SICON. arXiv:1802.06637**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**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.**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.**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**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**Briani A., Cardaliaguet P., Stable solutions in potential mean field game systems. NoDEA, 25(1):1, 2018. ArXiv:1612.01877**Cardaliaguet P., The convergence problem in mean field games with a local coupling. Appl. Math. Optim. (2017) 76, 177-215. arXiv:1610.06410**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*Armstrong S., Cardaliaguet P. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. To appear in JEMS. ArXiv**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**Cardaliaguet P., Hadikhanloo S. Learning in Mean Field Games: the Fictitious Play. COCV 23 (2017) 569--591. Arxiv**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**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**P. Cardaliaguet, C. Rainer, D. Rosenberg, N. Vieille, Markov games with frequent actions and incomplete information. To appear in Math. Oper. Res. Arxiv**Cardaliaguet P., Graber J., Mean field games systems of first order. ESAIM : COCV 21-3 (2015) 690---722. Arxiv**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**Armstrong S., Cardaliaguet P., Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations. Comm. Partial Differential Equations 40 (2015), no. 3, 540-600. Arxiv**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**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**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.**Cardaliaguet P., Long time average of first order mean field games and weak KAM theory. Dyn Games Appl (2013) 3:473—488 Arxiv**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**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.**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**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**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.**A differential game with a blind player. (with A. Souquière) Siam J. Control Opti. 50 (2012), 4, 2090—2116. Arxiv**Games with incomplete information in continuous time and for continuous types. (with Rainer C.) Dynamic Games and Applications, 2, 2 (2012), 206--227.**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.**Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients (with Cannarsa P). NoDEA, 19, 6 (2012), 751—769.**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.**Some Recent Aspects of Differential Game Theory. (with Buckdahn R., Quincampoix M.) Dyn. Games Appl (2011) 1, 74—114.**Optimal transport with convex obstacle.(with Jimenez C.) J. Math. Anal. Appl. 381 (2011), 43—63.**Viscosity solutions for a polymer crystal growth model (with O. Ley and A. Monteillet)*To appear in Indiana Univ. Math. J.*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.*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.*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.*A double obstacle problem arising in differential game theory.*J. Math. Anal. Appl. 360 (2009), no. 1, 95--107.*On a continuous time game with incomplete information. (with C. Rainer)*Math. Oper. Res. 34 (2009), no. 4, 769—794.*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.*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.*Uniqueness results for non-local Hamilton-Jacobi equations. (with G. Barles, O. Ley and A. Monteillet)*J. Functional Anal. 257, 5 (2009), 1261-1287.*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.*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.*(pdf) Stochastic differential games with asymmetric information (with C. Rainer).*Appl Math Optim (2009) 59: 1-36.*(pdf) A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable.*To appear in COCV.(

*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.*Deterministic differential games under probability knowledge of initial condition.*(with M. Quincampoix) Int. Game Theory Rev. 10 (2008), no. 1, 1--16.*(pdf)On the energy of a flow arising in shape optimization (with O. Ley).*Interfaces and Free Boundaries, 10 (2008), 221–241.*(pdf) Differential games with asymmetric information.**SIAM J. Control Optim.**46 (2007), no. 3, 816—838.**(pdf) Representation formulas for differential games with asymmetric information.*J. Optim. Theory Appl. 138 (2008), no. 1, 1--16.*(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.*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**(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).*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.(pdf)

*On some flows in shape optimization*(with O. Ley).*Arch. Ration. Mech. Anal.*183 (2007), no. 1, 21--58.(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.*Perimeter estimates for reachable sets of control systems*(with P. Cannarsa).*J. Convex Anal.*13 (2006), no. 2, 253--267.(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(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.(pdf)

*Supremal representation of L-infinity functionals*(with F. Prinari), Appl. Math. Optim. 52 (2005), no. 2, 129--141.(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.(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.*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)*(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.*(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.*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*(ps) On the strict concavity of the harmonic radius in dimension N2*(with R. Tahraoui), J.Math. Pures Appl.., 81 (2002) pp. 223-240.*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.*On front propagation problems with non local terms (Part II).*in `` J. Math. Anal. Appl. '' 260 (2001), pp. 572-601.*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.*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.*(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.*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.*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.*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.*(ps) On front propagation problems with non local terms.*in `` Advances Diff. Eq.'' Vol. 5, N. 1-3, (2000) pp:213-268.*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.*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.*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.*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.*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.*A differential game with two players and one target ``*SIAM J. Control and Optimization", Vol. 34, N. 4 (1996)

pp. 1441-1460.*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