January  2014, 1(1): 153-179. doi: 10.3934/jdg.2014.1.153

Structure of approximate solutions of dynamic continuous time zero-sum games

1. 

Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel

Received  April 2012 Revised  June 2012 Published  June 2013

In this paper we study a turnpike property of approximate solutions for a class of dynamic continuous-time two-player zero-sum games. These properties describe the structure of approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.
Citation: Alexander J. Zaslavski. Structure of approximate solutions of dynamic continuous time zero-sum games. Journal of Dynamics & Games, 2014, 1 (1) : 153-179. doi: 10.3934/jdg.2014.1.153
References:
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show all references

References:
[1]

in "Advances in Dynamic Game Theory," Ann. Internat. Soc. Dynam. Games, 9, Birkhäuser Boston, Boston, MA, (2007), 131-152. doi: 10.1007/978-0-8176-4553-3_7.  Google Scholar

[2]

Prentice-Hall, Inc., Englewood Cliffs, NJ, 1971.  Google Scholar

[3]

Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1984.  Google Scholar

[4]

Physica D, 8 (1983), 381-422. doi: 10.1016/0167-2789(83)90233-6.  Google Scholar

[5]

in "Advances in Dynamic Games and their Applications," Ann. Internat. Soc. Dynam. Games, 10, Birkhäuser Boston, Inc., Boston, MA, (2009), 3-18.  Google Scholar

[6]

Systems Control Lett., 56 (2007), 188-196. doi: 10.1016/j.sysconle.2006.08.011.  Google Scholar

[7]

J. Optim. Theory Appl., 106 (2000), 411-419. doi: 10.1023/A:1004611816252.  Google Scholar

[8]

ESAIM Control Optim. Calc. Var., 5 (2000), 279-292. doi: 10.1051/cocv:2000111.  Google Scholar

[9]

Automatica J. IFAC, 39 (2003), 1007-1010. doi: 10.1016/S0005-1098(03)00060-8.  Google Scholar

[10]

Applications of Mathematics (New York), 17, Springer-Verlag, New York, 1983.  Google Scholar

[11]

Set-Valued Anal., 6 (1998), 61-81. doi: 10.1023/A:1008606332037.  Google Scholar

[12]

Rev. of Econ. Studies, 34 (1967), 1-19. Google Scholar

[13]

SIAM J. Control Optim., 43 (2005), 2020-2035. doi: 10.1137/S0363012903404511.  Google Scholar

[14]

Bernoulli, 11 (2005), 1009-1029. doi: 10.3150/bj/1137421638.  Google Scholar

[15]

Appl. Math. Optim., 57 (2008), 349-369. doi: 10.1007/s00245-007-9025-6.  Google Scholar

[16]

SIAM J. Control Optim., 39 (2000), 1520-1539. doi: 10.1137/S0363012999361962.  Google Scholar

[17]

Dynamic Games and Applications, 2 (2012), 294-312. doi: 10.1007/s13235-012-0047-6.  Google Scholar

[18]

Appl. Math. and Opt., 13 (1985), 19-43. doi: 10.1007/BF01442197.  Google Scholar

[19]

Arch. Rational Mech. Anal., 106 (1989), 161-194. doi: 10.1007/BF00251430.  Google Scholar

[20]

J. Math. Anal. Appl., 340 (2008), 498-510. doi: 10.1016/j.jmaa.2007.08.008.  Google Scholar

[21]

Springer-Verlag, New York-Heidelberg, 1977.  Google Scholar

[22]

Ann. Inst. H. Poincaré, Anal. Non Linéaire, 16 (1999), 593-629. doi: 10.1016/S0294-1449(99)80029-8.  Google Scholar

[23]

Econometrica, 44 (1976), 841-865. doi: 10.2307/1911532.  Google Scholar

[24]

MIT press, Cambridge, MA, 2002.  Google Scholar

[25]

Automat. Remote Control, 50 (1989), 1333-1340.  Google Scholar

[26]

in "Optimal Control, Stabilization and Nonsmooth Analysis," Lecture Notes Control Inform. Sci., 301, Springer, Berlin, (2004), 121-132. doi: 10.1007/978-3-540-39983-4_8.  Google Scholar

[27]

Control Cybernet, 37 (2008), 451-468.  Google Scholar

[28]

Math. Methods Oper. Res., 61 (2005), 437-454. doi: 10.1007/s001860400392.  Google Scholar

[29]

American Economic Review, 55 (1965), 486-496. Google Scholar

[30]

Rev. Econ. Studies, 32 (1965), 85-104. Google Scholar

[31]

Math. USSR-Izvestiya, 29 (1987), 323-354. doi: 10.1070/IM1987v029n02ABEH000972.  Google Scholar

[32]

SIAM Journal on Control and Optimization, 3 (1995), 1643-1660, 1661-1686. doi: 10.1137/S036301299325726X.  Google Scholar

[33]

Nonlinear Analysis, 27 (1996), 895-931. doi: 10.1016/0362-546X(95)00029-U.  Google Scholar

[34]

Abstract and Applied Analysis, 4 (1999), 21-48. doi: 10.1155/S1085337599000020.  Google Scholar

[35]

Nonconvex Optimization and its Applications, 80, Springer, New York, 2006 .  Google Scholar

[36]

J. Convex Analysis, 15 (2008), 869-890.  Google Scholar

[37]

Springer Optimization and Its Applications, 44, Springer, New York, 2010. doi: 10.1007/978-0-387-88621-3.  Google Scholar

[38]

Journal of Nonlinear and Convex Analysis, 12 (2011), 49-68.  Google Scholar

[39]

Mathematics of Operations Research, 22 (1997), 726-746. doi: 10.1287/moor.22.3.726.  Google Scholar

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