Journal of Dynamics and Games (JDG)

A note on differential games with Pareto--optimal Nash equilibria: Deterministic and stochastic models
Pages: 195 - 203, Issue 3, July 2017

doi:10.3934/jdg.2017012      Abstract        References        Full text (357.8K)           Related Articles

Alejandra Fonseca-Morales - Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México City, 07000, Mexico (email)
Onésimo Hernández-Lerma - Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, Mexico (email)

1 R. Amir and N. Nannerup, Information structure and the tragedy of the commons in resource extraction, Journal of Bioeconomics, 8 (2006), 147-165.
2 T. Basar and Q. Zhu, Prices of anarchy, information, and cooperation, in differential games, Dyn Games Appl, 1 (2011), 50-73.       
3 L. D. Berkovitz and N. G. Medhin, Nonlinear Optimal Control Theory, CRC Press, Boca Raton, FL, 2013.       
4 J. Case, A class of games having Pareto optimal Nash equilibria, J Optim Theory Appl, 13 (1974), 379-385.       
5 C. D. Charalambous, Decentralized optimality conditions of stochastic differential decision problems via Girsanov's measure transformation, Math Control Signals Syst, 28 (2016), Art 19, 55 pp.       
6 C. Chiarella, M. C. Kemp, N. V. Long and K. Okuguchi, On the economics of international fisheries, Inter Econom Rev, 25 (1984), 85-92.       
7 J. E. Cohen, Cooperation and self-interest: Pareto-inefficiency of Nash equilibria in finite random games, Proc Natl Acad Sci USA, 95 (1998), 9724-9731.       
8 E. J. Dockner, S. Jorgensen, N. V. Long and G. Sorger, Differential Games in Economics and Management Science, Cambridge University Press, New York, 2000.       
9 E. J. Dockner and V. Kaitala, On efficient equilibrium solutions in dynamic games of resource management, Resour Energy, 11 (1989), 23-34.
10 P. Dubey, Inefficiency of Nash equilibria, Math Oper Res, 11 (1986), 1-8.       
11 J. C. Engwerda, Necessary and sufficient conditions for Pareto optimal solutions of cooperative differential games, SIAM J Control Optim, 48 (2010), 3859-3881.       
12 A. Fonseca-Morales and O. Hernández-Lerma, Potential differential games, Dyn. Games Appl., 7 (2017).       
13 D. González-Sánchez and O. Hernández-Lerma, Discrete-Time Stochastic Control and Dynamic Potential Games, Springer, New York, 2013.       
14 D. González-Sánchez and O. Hernández-Lerma, A survey of static and dynamic potential games, Sci China Math, 59 (2016), 2075-2102.       
15 R. Josa-Fombellida and J. P. Rincón-Zapatero, Euler-Lagrange equations of stochastic differential games: application to a game of a productive asset, Economic Theory, 59 (2015), 61-108.       
16 X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems, Birkhauser, Boston, 1995.       
17 N. V. Long, Dynamic games in the economics of natural resources: A survey, Dyn Games Appl, 1 (2011), 115-148.       
18 G. Martin-Herran and J. P. Rincón-Zapatero, Efficient Markov perfect Nash equilibria: Theory and application to dynamic fishery games, J Econom Dynam Control, 29 (2005), 1073-1096.       
19 P. V. Reddy and J. C. Engwerda, Necessary and sufficient conditions for Pareto optimality in infinite horizon cooperative differential games, IEEE Trans Autom Control, 59 (2014), 2536-2542.       
20 A. Seierstad, Pareto improvements of Nash equilibria in differential games, Dyn Games Appl, 4 (2014), 363-375.       
21 C. P. Simon and L. Blume, Mathematics for Economists, Norton & Co, New York, 1994.
22 F. Van Der Ploeg and A. J. de Zeeuw, International aspects of pollution control, Environmental and Resource Economics, 2 (1992), 117-139.
23 J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer, New York, 1999.       

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