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

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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.

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Acknowledgements

We thank Michèle Breton for the useful and heartfelt suggestions given to the authors during the Third Workshop on Dynamic Games in Management Science at HEC Montreal. The clarity of the paper has definitely been improved by the precise comments of the referees.

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Authors and Affiliations

  1. Department of Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    Alessandra Buratto, Luca Grosset & Bruno Viscolani

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  1. Alessandra Buratto
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  2. Luca Grosset
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  3. Bruno Viscolani
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Correspondence to Alessandra Buratto.

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Buratto, A., Grosset, L. & Viscolani, B. ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games. Dyn Games Appl 2, 269–279 (2012). https://doi.org/10.1007/s13235-012-0046-7

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  • DOI: https://doi.org/10.1007/s13235-012-0046-7

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