Degenerate Feedback and Time Consistency in Dynamic Games
This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as `perfect uncontrollable' and provide two examples based on (i) a model where firms invest so as to increase consumers' reservation prices, based upon Cellini and Lambertini (CEJOR, 2003); and (ii) a model where firms compete to increase their respective market shares, based upon Leitmann and Schmitendorf (IEEE Transactions on Automatic Control, 1978).
|Date of creation:||2005|
|Date of revision:|
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- Spence, Michael, 1976. "Product Differentiation and Welfare," American Economic Review, American Economic Association, vol. 66(2), pages 407-14, May.
- 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.
- Clemhout, S & Leitmann, G & Wan, H Y, Jr, 1971. "A Differential Game Model of Duopoly," Econometrica, Econometric Society, vol. 39(6), pages 911-38, November.
- Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
- Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
- Cellini, Roberto & Lambertini, Luca, 2002. "A differential game approach to investment in product differentiation," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 51-62, November.
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