On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games
AbstractIn this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, conditions for obtaining the coincidence between the Stackelberg and Nash equilibria are defined in terms of the instantaneous pay-off function and the state equation of the game. Secondly, it is showed that for a class of differential games with state-interdependence both equilibria are identical independently of the player being the leader of the game. A survey of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting in which differential games are defined. In this setting the first movement advantage of the leader may disappear and the both equilibria coincide.
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Bibliographic InfoPaper provided by Centro de Estudios Andaluces in its series Economic Working Papers at Centro de Estudios Andaluces with number E2003/40.
Length: 34 pages
Date of creation: 2003
Date of revision:
Differential games; stationary feedback Nash equilibrium; stationary feedback Stackelberg equilibrium.;
Other versions of this item:
- Santiago J. Rubio, 2002. "On The Coincidence Of The Feedback Nash And Stackelberg Equilibria In Economic Applications Of Differential Games," Working Papers. Serie AD 2002-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D62 - Microeconomics - - Welfare Economics - - - Externalities
- H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
- Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General
- Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
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- Fershtman, C. & Nitzan, S., 1988.
"Dynamic Voluntary Provision Of Public Goods,"
21-88, Tel Aviv.
- Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, April.
- Rubio, Santiago J. & Casino, Begona, 2001. "Competitive versus efficient extraction of a common property resource: The groundwater case," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1117-1137, August.
- Van Der Ploeg, F. & De Zeeuw, A.J., 1990.
"International Aspects Of Pollution Control,"
9065, Tilburg - Center for Economic Research.
- Ploeg, F. van der & Zeeuw, A.J. de, 1992. "International aspects of pollution control," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377516, Tilburg University.
- Ploeg, F. van der & Zeeuw, A.J. de, 1990. "International aspects of pollution control," Discussion Paper 1990-65, Tilburg University, Center for Economic Research.
- Tahvonen, Olli, 1996. "Trade with Polluting Nonrenewable Resources," Journal of Environmental Economics and Management, Elsevier, vol. 30(1), pages 1-17, January.
- Wirl, Franz & Dockner, Engelbert, 1995. "Leviathan governments and carbon taxes: Costs and potential benefits," European Economic Review, Elsevier, vol. 39(6), pages 1215-1236, June.
- Ploeg, F. van der & Zeeuw, A.J. de, 1988.
"Perfect equilibrium in a model of competitive arms accumulation,"
1988-4, Tilburg University, Center for Economic Research.
- van der Ploeg, F & de Zeeuw, A J, 1990. "Perfect Equilibrium in a Model of Competitive Arms Accumulation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 131-46, February.
- Ploeg, F. van der & Zeeuw, A.J. de, 1987. "Perfect equilibrium in a model of competitive arms accumulation," Research Memorandum 266, Tilburg University, Faculty of Economics and Business Administration.
- Ploeg, F. van der & Zeeuw , A.J. de, 1990. "Perfect equilibrium in a model of competitive arms accumulation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377522, Tilburg University.
- Dockner, Engelbert & Feichtinger, Gustav & Mehlmann, Alexander, 1989. "Noncooperative solutions for a differential game model of fishery," Journal of Economic Dynamics and Control, Elsevier, vol. 13(1), pages 1-20, January.
- Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October.
- Gradus, R.H.J.M., 1990. "Optimal dynamic profit taxation: The derivation of feedback Stackelberg equilibria," Research Memorandum 434, Tilburg University, Faculty of Economics and Business Administration.
- Jun-ichi Itaya & Koji Shimomura, 1999.
"A Dynamic Conjectural Variations Model in the Private Provision of Public Goods: a Differential Game Approach,"
Discussion Paper Series
104, Research Institute for Economics & Business Administration, Kobe University.
- Itaya, Jun-ichi & Shimomura, Koji, 2001. "A dynamic conjectural variations model in the private provision of public goods: a differential game approach," Journal of Public Economics, Elsevier, vol. 81(1), pages 153-172, July.
- Fershtman, Chaim & Muller, Eitan, 1984.
"Capital accumulation games of infinite duration,"
Journal of Economic Theory,
Elsevier, vol. 33(2), pages 322-339, August.
- Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-64, September.
- Franz Wirl, 1995. "The exploitation of fossil fuels under the threat of global warming and carbon taxes: A dynamic game approach," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 5(4), pages 333-352, June.
- Deger, Saadet & Sen, Somnath, 1984. "Optimal control and differential game models of military expenditure in less developed countries," Journal of Economic Dynamics and Control, Elsevier, vol. 7(2), pages 153-169, May.
- Tsutsui, Shunichi O., 1996. "Capacity constraints and voluntary output cutback in dynamic Cournot competition," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1683-1708.
- List, John A. & Mason, Charles F., 2001. "Optimal Institutional Arrangements for Transboundary Pollutants in a Second-Best World: Evidence from a Differential Game with Asymmetric Players," Journal of Environmental Economics and Management, Elsevier, vol. 42(3), pages 277-296, November.
- Simaan, M & Cruz, J B, Jr, 1975. "Formulation of Richardson's Model of Arms Race from a Differential Game Viewpoint," Review of Economic Studies, Wiley Blackwell, vol. 42(1), pages 67-77, January.
- Zagonari, Fabio, 1998. "International Pollution Problems: Unilateral Initiatives by Environmental Groups in One Country," Journal of Environmental Economics and Management, Elsevier, vol. 36(1), pages 46-69, July.
- Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
- Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
- Benhabib, Jess & Radner, Roy, 1992. "The Joint Exploitation of a Productive Asset: A Game-Theoretic Approach," Economic Theory, Springer, vol. 2(2), pages 155-90, April.
- Wirl Franz, 1994. "Pigouvian Taxation of Energy for Flow and Stock Externalities and Strategic, Noncompetitive Energy Pricing," Journal of Environmental Economics and Management, Elsevier, vol. 26(1), pages 1-18, January.
- Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
- Dockner, Engelbert J, 1992. "A Dynamic Theory of Conjectural Variations," Journal of Industrial Economics, Wiley Blackwell, vol. 40(4), pages 377-95, December.
- Piga, Claudio A. G., 2000. "Competition in a duopoly with sticky price and advertising," International Journal of Industrial Organization, Elsevier, vol. 18(4), pages 595-614, May.
- Rubio, Santiago J. & Escriche, Luisa, 2001.
"Strategic pigouvian taxation, stock externalities and polluting non-renewable resources,"
Journal of Public Economics,
Elsevier, vol. 79(2), pages 297-313, February.
- Santiago J. Rubio & Luisa Escriche, 1998. "- Strategic Pigouvian Taxation, Stock Externalities And Polluting Non-Renewable Resources," Working Papers. Serie EC 1998-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Driskill, Robert A. & McCafferty, Stephen, 1989. "Dynamic duopoly with adjustment costs: A differential game approach," Journal of Economic Theory, Elsevier, vol. 49(2), pages 324-338, December.
- Karray, Salma & Martín-Herrán, Guiomar, 2009. "A dynamic model for advertising and pricing competition between national and store brands," European Journal of Operational Research, Elsevier, vol. 193(2), pages 451-467, March.
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