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A strategic market game approach for the private provision of public goods
Turnpike properties of approximate solutions of dynamic discrete time zero-sum games
1. | Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel |
References:
[1] |
O. Alvarez and M. Bardi, Ergodic problems in differential games,, in Advances in Dynamic Game Theory, 9 (2007), 131.
doi: 10.1007/978-0-8176-4553-3_7. |
[2] |
J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis,, Wiley Interscience, (1984).
|
[3] |
S. Aubry and P. Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions I,, Physica D, 8 (1983), 381.
doi: 10.1016/0167-2789(83)90233-6. |
[4] |
M. Bardi, On differential games with long-time-average cost,, in Advances in Dynamic Games and their Applications, 10 (2009), 3.
|
[5] |
J. Blot and P. Cartigny, Optimality in infinite-horizon variational problems under sign conditions,, J. Optim. Theory Appl., 106 (2000), 411.
doi: 10.1023/A:1004611816252. |
[6] |
J. Blot and N. Hayek, Sufficient conditions for infinite-horizon calculus of variations problems,, ESAIM Control Optim. Calc. Var., 5 (2000), 279.
doi: 10.1051/cocv:2000111. |
[7] |
V. Gaitsgory and M. Quincampoix, Linear programming approach to deterministic infinite horizon optimal control problems with discounting,, SIAM J. Control and Optimization, 48 (2009), 2480.
doi: 10.1137/070696209. |
[8] |
M. K. Ghosh and K. S. Mallikarjuna Rao, Differential games with ergodic payoff,, SIAM J. Control Optim., 43 (2005), 2020.
doi: 10.1137/S0363012903404511. |
[9] |
H. Jasso-Fuentes and O. Hernandez-Lerma, Characterizations of overtaking optimality for controlled diffusion processes,, Appl. Math. Optim., 57 (2008), 349.
doi: 10.1007/s00245-007-9025-6. |
[10] |
O. Hernandez-Lerma and J. B. Lasserre, Zero-sum stochastic games in Borel spaces: Average payoff criteria,, SIAM J. Control Optim., 39 (2000), 1520.
doi: 10.1137/S0363012999361962. |
[11] |
V. Kolokoltsov and W. Yang, The turnpike theorems for Markov games,, Dynamic Games and Applications, 2 (2012), 294.
doi: 10.1007/s13235-012-0047-6. |
[12] |
A. Leizarowitz and V. J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics,, Arch. Rational Mech. Anal., 106 (1989), 161.
doi: 10.1007/BF00251430. |
[13] |
V. Lykina, S. Pickenhain and M. Wagner, Different interpretations of the improper integral objective in an infinite horizon control problem,, J. Math. Anal. Appl, 340 (2008), 498.
doi: 10.1016/j.jmaa.2007.08.008. |
[14] |
M. Marcus and A. J. Zaslavski, The structure of extremals of a class of second order variational problems,, Ann. Inst. H. Poincare, 16 (1999), 593.
doi: 10.1016/S0294-1449(99)80029-8. |
[15] |
L. W. McKenzie, Turnpike theory,, Econometrica, 44 (1976), 841.
doi: 10.2307/1911532. |
[16] |
B. S. Mordukhovich, Optimal control and feedback design of state-constrained parabolic systems in uncertainly conditions,, Appl. Analysis, 90 (2011), 1075.
doi: 10.1080/00036811003735840. |
[17] |
E. Ocana Anaya, P. Cartigny and P. Loisel, Singular infinite horizon calculus of variations. Applications to fisheries management,, J. Nonlinear Convex Anal., 10 (2009), 157.
|
[18] |
S. Pickenhain, V. Lykina and M. Wagner, On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems,, Control Cybernet, 37 (2008), 451.
|
[19] |
T. Prieto-Rumeau and O. Hernandez-Lerma, Bias and overtaking equilibria for zero-sum continuous-time Markov games,, Math. Methods Oper. Res., 61 (2005), 437.
doi: 10.1007/s001860400392. |
[20] |
P. A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule,, American Economic Review, 55 (1965), 486. Google Scholar |
[21] |
A. J. Zaslavski, Turnpike property for dynamic discrete time zero-sum games,, Abstract and Applied Analysis, 4 (1999), 21.
doi: 10.1155/S1085337599000020. |
[22] |
A. J. Zaslavski, Turnpike Properties in the Calculus of Variations and Optimal Control,, Springer, (2006).
|
[23] |
A. J. Zaslavski, The existence and structure of approximate solutions of dynamic discrete time zero-sum games,, Journal of Nonlinear and Convex Analysis, 12 (2011), 49.
|
[24] |
A. J. Zaslavski, Structure of Solutions of Variational Problems,, SpringerBriefs in Optimization, (2013).
doi: 10.1007/978-1-4614-6387-0. |
[25] |
A. J. Zaslavski and A. Leizarowitz, Optimal solutions of linear control systems with nonperiodic integrands,, Mathematics of Operations Research, 22 (1997), 726.
doi: 10.1287/moor.22.3.726. |
show all references
References:
[1] |
O. Alvarez and M. Bardi, Ergodic problems in differential games,, in Advances in Dynamic Game Theory, 9 (2007), 131.
doi: 10.1007/978-0-8176-4553-3_7. |
[2] |
J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis,, Wiley Interscience, (1984).
|
[3] |
S. Aubry and P. Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions I,, Physica D, 8 (1983), 381.
doi: 10.1016/0167-2789(83)90233-6. |
[4] |
M. Bardi, On differential games with long-time-average cost,, in Advances in Dynamic Games and their Applications, 10 (2009), 3.
|
[5] |
J. Blot and P. Cartigny, Optimality in infinite-horizon variational problems under sign conditions,, J. Optim. Theory Appl., 106 (2000), 411.
doi: 10.1023/A:1004611816252. |
[6] |
J. Blot and N. Hayek, Sufficient conditions for infinite-horizon calculus of variations problems,, ESAIM Control Optim. Calc. Var., 5 (2000), 279.
doi: 10.1051/cocv:2000111. |
[7] |
V. Gaitsgory and M. Quincampoix, Linear programming approach to deterministic infinite horizon optimal control problems with discounting,, SIAM J. Control and Optimization, 48 (2009), 2480.
doi: 10.1137/070696209. |
[8] |
M. K. Ghosh and K. S. Mallikarjuna Rao, Differential games with ergodic payoff,, SIAM J. Control Optim., 43 (2005), 2020.
doi: 10.1137/S0363012903404511. |
[9] |
H. Jasso-Fuentes and O. Hernandez-Lerma, Characterizations of overtaking optimality for controlled diffusion processes,, Appl. Math. Optim., 57 (2008), 349.
doi: 10.1007/s00245-007-9025-6. |
[10] |
O. Hernandez-Lerma and J. B. Lasserre, Zero-sum stochastic games in Borel spaces: Average payoff criteria,, SIAM J. Control Optim., 39 (2000), 1520.
doi: 10.1137/S0363012999361962. |
[11] |
V. Kolokoltsov and W. Yang, The turnpike theorems for Markov games,, Dynamic Games and Applications, 2 (2012), 294.
doi: 10.1007/s13235-012-0047-6. |
[12] |
A. Leizarowitz and V. J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics,, Arch. Rational Mech. Anal., 106 (1989), 161.
doi: 10.1007/BF00251430. |
[13] |
V. Lykina, S. Pickenhain and M. Wagner, Different interpretations of the improper integral objective in an infinite horizon control problem,, J. Math. Anal. Appl, 340 (2008), 498.
doi: 10.1016/j.jmaa.2007.08.008. |
[14] |
M. Marcus and A. J. Zaslavski, The structure of extremals of a class of second order variational problems,, Ann. Inst. H. Poincare, 16 (1999), 593.
doi: 10.1016/S0294-1449(99)80029-8. |
[15] |
L. W. McKenzie, Turnpike theory,, Econometrica, 44 (1976), 841.
doi: 10.2307/1911532. |
[16] |
B. S. Mordukhovich, Optimal control and feedback design of state-constrained parabolic systems in uncertainly conditions,, Appl. Analysis, 90 (2011), 1075.
doi: 10.1080/00036811003735840. |
[17] |
E. Ocana Anaya, P. Cartigny and P. Loisel, Singular infinite horizon calculus of variations. Applications to fisheries management,, J. Nonlinear Convex Anal., 10 (2009), 157.
|
[18] |
S. Pickenhain, V. Lykina and M. Wagner, On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems,, Control Cybernet, 37 (2008), 451.
|
[19] |
T. Prieto-Rumeau and O. Hernandez-Lerma, Bias and overtaking equilibria for zero-sum continuous-time Markov games,, Math. Methods Oper. Res., 61 (2005), 437.
doi: 10.1007/s001860400392. |
[20] |
P. A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule,, American Economic Review, 55 (1965), 486. Google Scholar |
[21] |
A. J. Zaslavski, Turnpike property for dynamic discrete time zero-sum games,, Abstract and Applied Analysis, 4 (1999), 21.
doi: 10.1155/S1085337599000020. |
[22] |
A. J. Zaslavski, Turnpike Properties in the Calculus of Variations and Optimal Control,, Springer, (2006).
|
[23] |
A. J. Zaslavski, The existence and structure of approximate solutions of dynamic discrete time zero-sum games,, Journal of Nonlinear and Convex Analysis, 12 (2011), 49.
|
[24] |
A. J. Zaslavski, Structure of Solutions of Variational Problems,, SpringerBriefs in Optimization, (2013).
doi: 10.1007/978-1-4614-6387-0. |
[25] |
A. J. Zaslavski and A. Leizarowitz, Optimal solutions of linear control systems with nonperiodic integrands,, Mathematics of Operations Research, 22 (1997), 726.
doi: 10.1287/moor.22.3.726. |
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