Fracking, renewables, and mean field games

SIAM Review

Volumn 59, Issue 3, 2017, Pages 588-615

  Chan, Patrick ^a   Sircar, Ronnie ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Energy markets; Exhaustible resources; Mean field games

Indexed keywords

CONTINUOUS TIME SYSTEMS; HYDRAULIC FRACTURING;

ALTERNATIVE ENERGY SOURCE; COURNOT COMPETITION; DIFFERENT ENERGY SOURCES; ENERGY MARKETS; EXHAUSTIBLE RESOURCES; MEAN FIELD GAMES; STRATEGIC DECISIONS; TECHNOLOGICAL INNOVATION;

SHALE OIL;

EID: 85031917196     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/15M1031424     Document Type: Article

References (27)

1. A. Bensoussan, J. Frehse, and P. Yam, Mean Field Games and Mean Field Type Control Theory, Springer, New York, 2013. (Cited on p. 594)
2. J. Bertrand, Théorie mathématique de la richesse sociale, Journal des Savants, 1883. (Cited on pp. 590, 593)
3. R. Carmona, J.-P. Fouque, and L.-H. Sun, Mean field games and systemic risk, Commun. Math. Sci., 13 (2015), pp. 911-933. (Cited on p. 594)
4. P. Chan and R. Sircar, Bertrand & Cournot mean field games, Appl. Math. Optim., 71 (2014), pp. 533-569. (Cited on pp. 590, 594, 595, 597, 598, 599, 600, 608, 612)
5. A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Chez L. Hachette, 1838. (Cited on pp. 590, 593)
6. A. Dasarathy and R. Sircar, Variable costs in dynamic Cournot energy markets, in Commodities, Energy and Environmental Finance, R. Aid, M. Ludkovski, and R. Sircar, eds., Fields Inst. Commun. 74, Fields Institute, Toronto, Springer, New York, 2015, pp. 397-430. (Cited on p. 604)
7. S. D. Deshmukh and S. R. Pliska, Optimal consumption and exploration of nonrenewable resources under uncertainty, Econometrica, 48 (1980), pp. 177-200. (Cited on p. 609)
8. E. Dockner, Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, UK, 2000. (Cited on p. 593)
9. D. A. Gomes, S. Patrizi, and V. Voskanyan, On the existence of classical solutions for stationary extended mean field games, Nonlinear Anal., 99 (2014), pp. 49-79. (Cited on p. 597)
10. D. A. Gomes and V. K. Voskanyan, Extended deterministic mean-field games, SIAM J. Control Optim., 54 (2016), pp. 1030-1055, https://doi.org/10.1137/130944503. (Cited on p. 597)
11. P. J. Graber and A. Bensoussan, Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games, preprint, https://arxiv.org/abs/1508.05408, 2015. (Cited on pp. 597, 612)
12. O. Guéant, Mean Field Games and Applications to Economics, Ph.D. thesis, Université Paris- Dauphine, France, 2009. (Cited on p. 594)
13. O. Guéant, J.-M. Lasry, and P.-L. Lions, Mean field games and applications, in Paris- Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Math. 200, Springer, Berlin, 2011, pp. 205-266. (Cited on p. 594)
14. C. Harris, S. Howison, and R. Sircar, Games with exhaustible resources, SIAM J. Appl. Math., 70 (2010), pp. 2556-2581, https://doi.org/10.1137/09076862X. (Cited on pp. 590, 593, 596, 597, 601)
15. H. Hotelling, The economics of exhaustible resources, J. Political Economy, 39 (1931), pp. 137-175. (Cited on p. 593)
16. M. Huang, P. E. Caines, and R. P. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and Nash equilibrium solutions, in Proceedings of the 42nd IEEE Conference on Decision and Control, IEEE, 2003, pp. 98-103. (Cited on pp. 588, 590, 594)
17. M. Huang, R. P. Malhamé, and P. E. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst., 6 (2006), pp. 221-252. (Cited on pp. 588, 590, 594)
18. X. Huang, S. Jaimungal, and M. Nourian, Mean-Field Game Strategies for Optimal Execution, preprint, https://doi.org/10.2139/ssrn.2578733, 2017. (Cited on p. 594)
19. J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math., 2 (2007), pp. 229-260. (Cited on pp. 588, 590, 593, 596)
20. A. Ledvina and R. Sircar, Dynamic Bertrand oligopoly, Appl. Math. Optim., 63 (2011), pp. 11-44. (Cited on pp. 590, 593, 595)
21. A. Ledvina and R. Sircar, Oligopoly games under asymmetric costs and an application to energy production, Math. Financ. Econ., 6 (2012), pp. 261-293. (Cited on p. 593)
22. R. E. Lucas and B. Moll, Knowledge Growth and the Allocation of Time, Tech. Report, National Bureau of Economic Research, https://doi.org/10.3386/w17495, 2011. (Cited on pp. 594, 610)
23. M. Ludkovski and R. Sircar, Exploration and exhaustibility in dynamic Cournot games, European J. Appl. Math., 23 (2012), pp. 343-372. (Cited on pp. 593, 609, 610)
24. M. Ludkovski and R. Sircar, Game theoretic models for energy production, in Commodities, Energy and Environmental Finance, R. Aid, M. Ludkovski, and R. Sircar, eds., Fields Inst. Commun. 74, Fields Institute, Toronto, Springer, New York, 2015, pp. 317-333. (Cited on p. 593)
25. M. Ludkovski and R. Sircar, Technology ladders and R&D in dynamic Cournot markets, J. Econom. Dynam. Control, 69 (2016), pp. 127-151. (Cited on p. 596)
26. M. Ludkovski and X. Yang, Dynamic Cournot models for production of exhaustible commodities under stochastic demand, in Commodities, Energy and Environmental Finance, R. Aid, M. Ludkovski, and R. Sircar, eds., Fields Inst. Commun. 74, Fields Institute, Toronto, Springer, New York, 2015, pp. 371-396. (Cited on p. 593)
27. R. S. Pindyck, The optimal exploration and production of nonrenewable resources, J. Political Economy, 86 (1978), pp. 841-861. (Cited on p. 593)