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Pure and Random strategies in differential game with incomplete informations
1. | CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75016 Paris, France |
2. | Laboratoire de Mathématiques de Bretagne Atlantique, CNRS-UMR 6205, Université de Brest, 6, avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3, France, France |
References:
[1] |
L. Ambrosio, Lecture Notes on Optimal Transport Problems, Mathematical Aspects of Evolving Interfaces, CIME Summer School in Madeira, Vol. 1812, Springer, 2003.
doi: 10.1007/978-3-540-39189-0_1. |
[2] |
R. J. Aumann, Mixed and behavior strategies in infinite extensive games, in Advances in Game Theory, Princeton Univ. Press, Princeton, N.J., 1964, 627-650. |
[3] |
R. J. Aumann and M. B. Maschler, Repeated Games with Incomplete Information, MIT Press, Cambridge, MA, 1995. |
[4] |
R. Buckdahn, P. Cardaliaguet and M. Quincampoix, Some recent aspects of differential game theory, Dynamic Games Applications, 1 (2011), 74-114.
doi: 10.1007/s13235-010-0005-0. |
[5] |
R. Buckdahn, J. Li and M. Quincampoix, Value function of differential games without isaacs conditions. An approach with non-anticipative mixed strategies, Internat. J. of Game Theory, 42 (2013), 989-1020.
doi: 10.1007/s00182-012-0351-9. |
[6] |
P. Cardaliaguet, Differential games with asymmetric information, SIAM J. Control Optim., 46 (2007), 816-838.
doi: 10.1137/060654396. |
[7] |
P. Cardaliaguet and M. Quincampoix, Deterministic differential games under probability knowledge of initial condition, Int. Game Theory Rev., 10 (2008), 1-16.
doi: 10.1142/S021919890800173X. |
[8] |
P. Cardaliaguet and C. Rainer, Stochastic differential games with assymetric information, Appl. Math. Optim., 59 (2009), 1-36.
doi: 10.1007/s00245-008-9042-0. |
[9] |
P. Cardaliaguet and C. Rainer, Games with incomplete information in continuous time and for continuous types, Dyn. Games Appl., 2 (2012), 206-227.
doi: 10.1007/s13235-012-0043-x. |
[10] |
C. Dellacherie and P. A. Meyer, Probabilities and Potential, North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam, 1978. |
[11] |
J. F. Mertens, S. Sorin and S. Zamir, Repeated Games, CORE Discussion Papers 9420, 9421, 9422, 1994.
doi: 10.1057/9780230226203.3424. |
[12] |
A. Pratelli, On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation, Ann. Inst. H. Poincaré Probab. Statist., 43 (2007), 1-13.
doi: 10.1016/j.anihpb.2005.12.001. |
[13] |
D. Schmeidler, Equilibrium points of nonatomic games, Journal of Statistical Physics, 7 (1973), 295-300.
doi: 10.1007/BF01014905. |
[14] |
C. Villani, Topics in Optimal Transportation, Graduate studies in Mathematics, Vol. 58, AMS, 2003.
doi: 10.1007/b12016. |
show all references
References:
[1] |
L. Ambrosio, Lecture Notes on Optimal Transport Problems, Mathematical Aspects of Evolving Interfaces, CIME Summer School in Madeira, Vol. 1812, Springer, 2003.
doi: 10.1007/978-3-540-39189-0_1. |
[2] |
R. J. Aumann, Mixed and behavior strategies in infinite extensive games, in Advances in Game Theory, Princeton Univ. Press, Princeton, N.J., 1964, 627-650. |
[3] |
R. J. Aumann and M. B. Maschler, Repeated Games with Incomplete Information, MIT Press, Cambridge, MA, 1995. |
[4] |
R. Buckdahn, P. Cardaliaguet and M. Quincampoix, Some recent aspects of differential game theory, Dynamic Games Applications, 1 (2011), 74-114.
doi: 10.1007/s13235-010-0005-0. |
[5] |
R. Buckdahn, J. Li and M. Quincampoix, Value function of differential games without isaacs conditions. An approach with non-anticipative mixed strategies, Internat. J. of Game Theory, 42 (2013), 989-1020.
doi: 10.1007/s00182-012-0351-9. |
[6] |
P. Cardaliaguet, Differential games with asymmetric information, SIAM J. Control Optim., 46 (2007), 816-838.
doi: 10.1137/060654396. |
[7] |
P. Cardaliaguet and M. Quincampoix, Deterministic differential games under probability knowledge of initial condition, Int. Game Theory Rev., 10 (2008), 1-16.
doi: 10.1142/S021919890800173X. |
[8] |
P. Cardaliaguet and C. Rainer, Stochastic differential games with assymetric information, Appl. Math. Optim., 59 (2009), 1-36.
doi: 10.1007/s00245-008-9042-0. |
[9] |
P. Cardaliaguet and C. Rainer, Games with incomplete information in continuous time and for continuous types, Dyn. Games Appl., 2 (2012), 206-227.
doi: 10.1007/s13235-012-0043-x. |
[10] |
C. Dellacherie and P. A. Meyer, Probabilities and Potential, North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam, 1978. |
[11] |
J. F. Mertens, S. Sorin and S. Zamir, Repeated Games, CORE Discussion Papers 9420, 9421, 9422, 1994.
doi: 10.1057/9780230226203.3424. |
[12] |
A. Pratelli, On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation, Ann. Inst. H. Poincaré Probab. Statist., 43 (2007), 1-13.
doi: 10.1016/j.anihpb.2005.12.001. |
[13] |
D. Schmeidler, Equilibrium points of nonatomic games, Journal of Statistical Physics, 7 (1973), 295-300.
doi: 10.1007/BF01014905. |
[14] |
C. Villani, Topics in Optimal Transportation, Graduate studies in Mathematics, Vol. 58, AMS, 2003.
doi: 10.1007/b12016. |
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