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ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games

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  • Alessandra Buratto
  • Luca Grosset
  • Bruno Viscolani

Abstract

Open-loop Stackelberg equilibria in linear-state games are subgame perfect. This result holds under the hypothesis of unconstrained final state; whereas we need to take into account suitable final-state conditions in order to correctly formalize certain economic problems. A striking contribution of this paper is that it tackles the consistency problem for an open-loop Stackelberg equilibrium in linear-state games with a final-state constraint in the leader’s problem. In this paper, after proving that such a type of equilibrium is not subgame perfect, we introduce a weaker definition of subgame perfectness, which we call ε-subgame perfectness. This new definition can be applied to the open-loop Stackelberg equilibrium of a constrained linear-state game. Finally, we present some explanatory examples to show how the definition of ε-subgame perfectness can be meaningful. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Alessandra Buratto & Luca Grosset & Bruno Viscolani, 2012. "ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 269-279, September.
    • Handle: RePEc:spr:dyngam:v:2:y:2012:i:3:p:269-279
    DOI: 10.1007/s13235-012-0046-7
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
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    6. repec:dau:papers:123456789/6046 is not listed on IDEAS
    7. R. Cellini & L. Lambertini & G. Leitmann, 2005. "Degenerate Feedback and Time Consistency in Dynamic Games," Working Papers 535, Dipartimento Scienze Economiche, Universita' di Bologna.
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    Cited by:

    1. El Ouardighi, Fouad, 2014. "Supply quality management with optimal wholesale price and revenue sharing contracts: A two-stage game approach," International Journal of Production Economics, Elsevier, vol. 156(C), pages 260-268.

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