Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games
Envelope theorems are established for locally differentiable Stackelberg equilibria of a general class of finite horizon differential games with an open-loop information structure. It is shown that the follower's envelope results agree in form with those of any player in an open-loop Nash equilibrium, while those of the leader differ. An unanticipated conclusion is that the costate vector of the leader--but not that of the follower--corresponding to the state vector of the differential game may be legitimately interpreted as the shadow value of the state vector for time-inconsistent open-loop Stackelberg equilibria. Surprisingly, the same cannot be said for time-consistent open-loop Stackelberg equilibria.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kort, P.M. & Jorgensen, S. & van Schijndel, G.J.C.T., 1989.
"Optimal investment, financing and dividends : A Stackelberg differential game,"
Other publications TiSEM
f8732288-14f7-4fe6-963e-9, Tilburg University, School of Economics and Management.
- Jorgensen, Steffen & Kort, Peter M. & Van Schijndel, Geert-Jan C. Th., 1989. "Optimal investment, financing, and dividends : A stackelberg differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 13(3), pages 339-377, July.
- Joergensen, S. & Kort, P.M. & van Schijndel, G.J.C.T., 1987. "Optimal investment, financing and dividends : A Stackelberg differential game," Research Memorandum FEW 286, Tilburg University, School of Economics and Management.
- Xie, Danyang, 1997.
"On Time Inconsistency: A Technical Issue in Stackelberg Differential Games,"
Journal of Economic Theory,
Elsevier, vol. 76(2), pages 412-430, October.
- Danyang Xie, 2002. "On Time Inconsistency: A Technical Issue in Stackelberg Differential Games," Macroeconomics 0212004, EconWPA.
- Jeffrey Ely & Drew Fudenberg & David K. Levine, 2004.
"When is Reputation Bad?,"
Harvard Institute of Economic Research Working Papers
2035, Harvard - Institute of Economic Research.
- Jeffery Ely & Drew Fudenberg & David Levine, 2002. "When is Reputation Bad?," Discussion Papers 1358, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jeffrey Ely & Drew Fudenberg & David K. Levine, 2002. "When is Reputation Bad?," Harvard Institute of Economic Research Working Papers 1962, Harvard - Institute of Economic Research.
- Levine, David & Ely, Jeffrey & Fudenberg, Drew, 2008. "When is Reputation Bad?," Scholarly Articles 3196337, Harvard University Department of Economics.
- Jeffrey Ely & Drew Fudenberg & David K Levine, 2005. "When is Reputation Bad," Levine's Working Paper Archive 618897000000000016, David K. Levine.
- Morgan, John & VÃ¡rdy, Felix, 2005.
"The Value of Commitment in Contests and Tournaments when Observation is Costly,"
Competition Policy Center, Working Paper Series
qt0s6752rf, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
- Morgan, John & Vardy, Felix, 2007. "The value of commitment in contests and tournaments when observation is costly," Games and Economic Behavior, Elsevier, vol. 60(2), pages 326-338, August.
- Felix Várdy & John Morgan, 2005. "The Value of Commitment in Contests and Tournaments when Observation is Costly," Public Economics 0504005, EconWPA.
- A. Michael Spence, 1979. "Investment Strategy and Growth in a New Market," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 1-19, Spring.
- Eilon Solan & Leeat Yariv, 1998.
"Games with Espionage,"
1257, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Cremer, Jacques, & Riordan, Michael H, 1985. "A Sequential Solution to the Public Goods Problem," Econometrica, Econometric Society, vol. 53(1), pages 77-84, January.
- Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2007. "Stackelberg games and multiple equilibrium behaviors on networks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 841-861, October.
- Caputo, Michael R., 1992. "Fundamental symmetries and qualitative properties in the adjustment cost model of the firm," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 99-112.
- Caputo, Michael R., 1998. "A dual vista of the Stackelberg duopoly reveals its fundamental qualitative structure," International Journal of Industrial Organization, Elsevier, vol. 16(3), pages 333-352, May.
- Caputo, Michael R., 2007. "The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 198-224, November.
- repec:spr:pharme:v:22:y:2004:i:4:p:225-244 is not listed on IDEAS
- repec:ebl:ecbull:v:12:y:2006:i:12:p:1-9 is not listed on IDEAS
- 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, November.
- Amitrajeet A. Batabyal & Hamid Beladi, 2006. "A Stackelberg Game Model of Trade in Renewable Resources with Competitive Sellers," Review of International Economics, Wiley Blackwell, vol. 14(1), pages 136-147, 02.
- Koji Shimomura & Danyang Xie, 2008. "Advances on Stackelberg open-loop and feedback strategies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 115-133.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:34:y:2010:i:6:p:1123-1139. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.