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Linear quadratic differential games with mixed leadership: The open-loop solution
1. | Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, TX 75080-3021, United States, United States, United States |
References:
[1] |
T. Başar, On the relative leadership property of Stackelberg strategies, J. Optimization Theory and Applications, 11 (1973), 655-661.
doi: 10.1007/BF00935564. |
[2] |
T. Başar and A. Haurie, Feedback equilibria in differential games with structural and modal uncertainties, in "Advances in Large Scale Systems" (eds. J. B. Cruz, Jr.), JAE Press Inc., (1984), 163-201. |
[3] |
T. Başar, A. Haurie and G. Ricci, On the dominance of capitalists' leadership in a feedback Stackelberg solution of a differential game model of capitalism, J. Economic Dynamics and Control, 9 (1985), 101-125.
doi: 10.1016/0165-1889(85)90026-0. |
[4] |
T. Başar and G. J. Olsder, "Dynamic Noncooperative Game Theory," 2nd edition, Academic Press, New York, 1995. |
[5] |
T. Başar, A. Bensoussan and S. P. Sethi, Differential games with mixed leadership: the open-loop solution, Applied Mathematics and Computation, 217 (2010), 972-979.
doi: 10.1016/j.amc.2010.01.048. |
[6] |
A. Bensoussan, S. Chen and S. P. Sethi, Feedback Stackelberg solutions of infinite-horizon stochastic differential games, forthcoming. |
[7] |
A. Bensoussan, S. Chen and S. P. Sethi, The maximum principle for global solutions of stochastic Stackelberg differential games, working paper. |
[8] |
G. F. Cachon, Supply chain coordination with contracts, in "Handbooks in OR and MS Vol. 11, SCM: Design, Coordination and Cooperation" (eds. A. G. De Kok and S. C. Graves), Elsevier, (2003), 227-339. |
[9] |
A. Chutani and S. P. Sethi, Cooperative advertising in a dynamic retail market oligopoly, Dynamic Games and Applications, 2012, forthcoming.
doi: 10.1007/s13235-012-0053-8. |
[10] |
A. Chutani and S. P. Sethi, Optimal advertising and pricing in a dynamic durable goods supply chain, Journal of Optimization Theory and Applications, 154 (2012), 615-643.
doi: 10.1007/s10957-012-0034-5. |
[11] |
E. Dockner, S. Jøgensen, N. V. Long and G. Sorger, "Differential Games in Economics and Management Science," Cambridge University Press, Cambridge, UK, 2000.
doi: 10.1017/CBO9780511805127. |
[12] |
X. He, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Retail competition and cooperative advertising, Operations Research Letters, 39 (2011), 11-16.
doi: 10.1016/j.orl.2010.10.006. |
[13] |
X. He, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Co-Op advertising in dynamic retail oligopolies, Decision Sciences, 43 (2012), 73-105.
doi: 10.1111/j.1540-5915.2011.00336.x. |
[14] |
X. He, A. Prasad and S. P. Sethi, Cooperative advertising and pricing in a dynamic stochastic supply chain: feedback stackelberg strategies, Production and Operations Management, 18 (2009), 78-94. |
[15] |
X. He, A. Prasad, S. P. Sethi and G. J. Gutierrez, A survey of Stackelberg differential game models in supply chain and marketing channels, J. Systems Science and Systems Engineering, 16 (2007), 385-413.
doi: 10.1007/s11518-007-5058-2. |
[16] |
A. Krishnamoorthy, A. Prasad and S. P. Sethi, Optimal pricing and advertising in a durable-good duopoly, European Journal of Operations Research, 200 (2010), 486-497.
doi: 10.1016/j.ejor.2009.01.003. |
[17] |
G. Leitmann, On generalized Stackelberg strategies, J. Optimization Theory and Applications, 26 (1978), 637-643.
doi: 10.1007/BF00933155. |
[18] |
E. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs, Probab. Theory Relat. Fields, 114 (1999), 123-150.
doi: 10.1007/s004409970001. |
[19] |
A. Prasad, S. P. Sethi and P. A. Naik, Understanding the impact of churn in dynamic oligopoly markets, Automatica, 48 (2012), 2882-2887.
doi: 10.1016/j.automatica.2012.08.031. |
[20] |
M. Simaan and J. B. Cruz, Jr., On the Stackelberg strategy in nonzero-sum games, J. Optimization Theory and Applications, 11 (1973), 533-555.
doi: 10.1007/BF00935665. |
[21] |
M. Simaan and J. B. Cruz, Jr., Additional aspects of the Stackelberg strategy in nonzero-sum games, J. Optimization Theory and Applications, 11 (1973b), 613-626.
doi: 10.1007/BF00935561. |
[22] |
H. von Stackelberg, "Marktform und Gleichgewicht," Springer, Vienna, 1934 (An English translation appeared in "The Theory of the Market Economy," Oxford University Press, New York, 1952). |
[23] |
S. Tang, General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations, SIAM J. Control Optim., 42 (2003), 53-75.
doi: 10.1137/S0363012901387550. |
[24] |
J. Yong, Linear forward-backward stochastic differential equations with random coefficients, Probab. Theory Relat. Fields, 135 (2006), 53-83.
doi: 10.1007/s00440-005-0452-5. |
show all references
References:
[1] |
T. Başar, On the relative leadership property of Stackelberg strategies, J. Optimization Theory and Applications, 11 (1973), 655-661.
doi: 10.1007/BF00935564. |
[2] |
T. Başar and A. Haurie, Feedback equilibria in differential games with structural and modal uncertainties, in "Advances in Large Scale Systems" (eds. J. B. Cruz, Jr.), JAE Press Inc., (1984), 163-201. |
[3] |
T. Başar, A. Haurie and G. Ricci, On the dominance of capitalists' leadership in a feedback Stackelberg solution of a differential game model of capitalism, J. Economic Dynamics and Control, 9 (1985), 101-125.
doi: 10.1016/0165-1889(85)90026-0. |
[4] |
T. Başar and G. J. Olsder, "Dynamic Noncooperative Game Theory," 2nd edition, Academic Press, New York, 1995. |
[5] |
T. Başar, A. Bensoussan and S. P. Sethi, Differential games with mixed leadership: the open-loop solution, Applied Mathematics and Computation, 217 (2010), 972-979.
doi: 10.1016/j.amc.2010.01.048. |
[6] |
A. Bensoussan, S. Chen and S. P. Sethi, Feedback Stackelberg solutions of infinite-horizon stochastic differential games, forthcoming. |
[7] |
A. Bensoussan, S. Chen and S. P. Sethi, The maximum principle for global solutions of stochastic Stackelberg differential games, working paper. |
[8] |
G. F. Cachon, Supply chain coordination with contracts, in "Handbooks in OR and MS Vol. 11, SCM: Design, Coordination and Cooperation" (eds. A. G. De Kok and S. C. Graves), Elsevier, (2003), 227-339. |
[9] |
A. Chutani and S. P. Sethi, Cooperative advertising in a dynamic retail market oligopoly, Dynamic Games and Applications, 2012, forthcoming.
doi: 10.1007/s13235-012-0053-8. |
[10] |
A. Chutani and S. P. Sethi, Optimal advertising and pricing in a dynamic durable goods supply chain, Journal of Optimization Theory and Applications, 154 (2012), 615-643.
doi: 10.1007/s10957-012-0034-5. |
[11] |
E. Dockner, S. Jøgensen, N. V. Long and G. Sorger, "Differential Games in Economics and Management Science," Cambridge University Press, Cambridge, UK, 2000.
doi: 10.1017/CBO9780511805127. |
[12] |
X. He, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Retail competition and cooperative advertising, Operations Research Letters, 39 (2011), 11-16.
doi: 10.1016/j.orl.2010.10.006. |
[13] |
X. He, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Co-Op advertising in dynamic retail oligopolies, Decision Sciences, 43 (2012), 73-105.
doi: 10.1111/j.1540-5915.2011.00336.x. |
[14] |
X. He, A. Prasad and S. P. Sethi, Cooperative advertising and pricing in a dynamic stochastic supply chain: feedback stackelberg strategies, Production and Operations Management, 18 (2009), 78-94. |
[15] |
X. He, A. Prasad, S. P. Sethi and G. J. Gutierrez, A survey of Stackelberg differential game models in supply chain and marketing channels, J. Systems Science and Systems Engineering, 16 (2007), 385-413.
doi: 10.1007/s11518-007-5058-2. |
[16] |
A. Krishnamoorthy, A. Prasad and S. P. Sethi, Optimal pricing and advertising in a durable-good duopoly, European Journal of Operations Research, 200 (2010), 486-497.
doi: 10.1016/j.ejor.2009.01.003. |
[17] |
G. Leitmann, On generalized Stackelberg strategies, J. Optimization Theory and Applications, 26 (1978), 637-643.
doi: 10.1007/BF00933155. |
[18] |
E. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs, Probab. Theory Relat. Fields, 114 (1999), 123-150.
doi: 10.1007/s004409970001. |
[19] |
A. Prasad, S. P. Sethi and P. A. Naik, Understanding the impact of churn in dynamic oligopoly markets, Automatica, 48 (2012), 2882-2887.
doi: 10.1016/j.automatica.2012.08.031. |
[20] |
M. Simaan and J. B. Cruz, Jr., On the Stackelberg strategy in nonzero-sum games, J. Optimization Theory and Applications, 11 (1973), 533-555.
doi: 10.1007/BF00935665. |
[21] |
M. Simaan and J. B. Cruz, Jr., Additional aspects of the Stackelberg strategy in nonzero-sum games, J. Optimization Theory and Applications, 11 (1973b), 613-626.
doi: 10.1007/BF00935561. |
[22] |
H. von Stackelberg, "Marktform und Gleichgewicht," Springer, Vienna, 1934 (An English translation appeared in "The Theory of the Market Economy," Oxford University Press, New York, 1952). |
[23] |
S. Tang, General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations, SIAM J. Control Optim., 42 (2003), 53-75.
doi: 10.1137/S0363012901387550. |
[24] |
J. Yong, Linear forward-backward stochastic differential equations with random coefficients, Probab. Theory Relat. Fields, 135 (2006), 53-83.
doi: 10.1007/s00440-005-0452-5. |
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