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S-adapted Equilibria in Games Played Over Event Trees with Coupled Constraints

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Abstract

This article deals with the general theory of games played over uncontrolled event trees, i.e., games where the transition from one node to another is nature’s decision and cannot be influenced by the players’ actions. The solution concept for this class of games was introduced under the name of S-adapted equilibrium, where S stands for sample of realizations of the random process. In this paper, it is assumed that the players also face a coupled constraint at each node, and therefore the relevant solution concept is the normalized equilibrium à la Rosen. Existence and uniqueness conditions for this equilibrium are provided, as well as a stochastic-control formulation of the game and a maximum principle. A simple illustrative example in environmental economics is presented.

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Notes

  1. We heavily draw on Haurie et al. [5] for the description of this class of games.

  2. The results of this scenario are available from the authors upon request.

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Acknowledgments

We would like to thank the two anonymous Reviewers  and  Professor George Leitmann for their helpful comments. The research was supported by NSERC and SSRHC, Canada

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Authors and Affiliations

  1. GERAD, HEC Montréal, Montréal,  H3T 2A7,  Canada

    Elnaz Kanani Kuchesfehani

  2. Chair in Game Theory and Management, GERAD, HEC Montréal, Montréal , H3T 2A7, Canada

    Georges Zaccour

Authors
  1. Elnaz Kanani Kuchesfehani
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  2. Georges Zaccour
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Correspondence to Georges Zaccour.

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Communicated by Francesco Zirilli.

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Kuchesfehani , E.K., Zaccour, G. S-adapted Equilibria in Games Played Over Event Trees with Coupled Constraints. J Optim Theory Appl 166, 644–658 (2015). https://doi.org/10.1007/s10957-014-0623-6

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  • DOI: https://doi.org/10.1007/s10957-014-0623-6

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