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On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games

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Abstract

In 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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Paper provided by Centro de Estudios Andaluces in its series Economic Working Papers at Centro de Estudios Andaluces with number E2003/40.

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Length: 34 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:cea:doctra:e2003_40

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Keywords: Differential games; stationary feedback Nash equilibrium; stationary feedback Stackelberg equilibrium.;

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Cited by:
  1. 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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