Abstract
This paper exposes in voluntarily simple terms the concept of S-adapted equilibrium introduced to represent and compute economic equilibria on stochastic markets. A model of the European gas market, that has been at the origin of the introduction of the concept, is recalled in this paper and the results obtained in 1987, when the contingent equilibrium has been computed for a time horizon extending until 2020, are compared with the observed trend in these markets over the last two decades. The information structure subsumed by this concept of S-adapted strategies is then analyzed, using different paradigms of dynamic games. The paper terminates with some open and intriguing questions related to the time consistency and subgame perfectness of the dynamic equilibrium thus introduced.
The research of this author has been supported by an SNSF grant
The research of this author has been supported by an NSERC grant.
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References
Başar T., Time consistency and robustness of equilibria in noncooperative dynamic games in F. van der Ploeg and A. J. de Zeeuw (eds.) Dynamic Policy Games in Economics, North Holland, Amsterdam, 1989.
Birge J.R. and Louveaux F., Introduction to Stochastic Programming Springer Series in Operations Research. Springer-Verlag, New York, 1997.
Carlson D. and Haurie A., Infinite horizon dynamic games with coupled state constraints, in J.A. filar, V. Gaitsgory and K. Misukami (eds.) Advances in dynamic games and applications, Annals of the International Society of Dynamic Games, Vol. 5, pp. 195–212, Birkhäuser, Boston, 2000.
Friedman J.W., Game Theory with Economic Applications, Oxford University Press, Oxford, 1986.
Fudenberg D. and Tirole J., Game Theory, MIT Press, Cambridge, MA 1991.
Gürkan G., Özge A. Y. and Robinson S. M., Sample-path solution of stochastic variational inequalities, Mathematical Programming, 84 (1999), pp. 313–333.
Haurie A., Piecewise deterministic differential games, in T. Baçar and P. Bernhard (eds.) Differential Games and Applications, Lecture Notes in Control and Information Sciences, Vol. 119, Springer-Verlag, Berlin, 1989.
Haurie A., Environmental coordination in dynamic oligopolistic markets, Group Decision and Negotiations, Vol. 4, pp. 49–67, 1995.
Haurie A. and Moresino F., Computation of S-adapted equilibria in piecewise deterministic games via stochastic programming methods, Annals of the International Society of Dynamic Games, Vol. 6, pp. 225–252, Birkhäuser, Cambridge, MA, 2001.
Haurie A. and Moresino F., S-Adapted Oligopoly Equilibria and Approximations in Stochastic Variational Inequalities, Annals of Operations Research, to appear.
Haurie A., Roche M., Turnpikes and computation of piecewsie open-loop equilibria in stochastic differential games, Journal of Economic Dynamics and Control, Vol. 18, pp. 317–344, 1994.
Haurie A., Zaccour G., Differential game models of global environmental management, in C. Carrara and J.A. Filar eds., Control and game-theoretic models of the environment, Annals of the International Society of Dynamic Games, Vol. 2, pp. 3–23, Birkhäuser, Boston, 1995.
Haurie A., Zaccour G., Legrand J. and Smeers Y., A stochastic dynamic Nash-Cournot model for the European gas market, Cahiers du GERAD, No. G-87-24, October 1987.
Haurie A., Zaccour G., Legrand J. and Smeers Y., Unmodèle de Nash Cournot stochastique et dynamique pour le marché européen du gaz, in Actes du colloque Modélisation et analyse des marchés du gaz naturel, HEC, Montréal, 1988.
Haurie A., Zaccour G. and Smeers Y., Stochastic equilibrium programming for dynamic oligopolistic markets, Journal of Optimization Theory and Applications, vol. 66, No. 2, 243–253, 1990.
Kuhn H.W., Extensive games and the problem of information, in H.W. Kuhn and A.W. Tucker (eds.), Contributions to the theory of games, Vol. 2, Annals of Mathematical Studies No 28, Princeton University Press, Princeton, New Jersey, 1953, pp. 193–216.
Rosen J. B., Existence and uniqueness of equilibrium points for concave Nperson games, Econometrica, vol. 33, 1965, pp. 520–534.
Selten R., Rexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory, Vol. 4, 1975, pp. 25–55.
Zaccour G., Théorie des jeux et marchés énergétiques: marché européen de gaz naturel et échanges d’électricité, PhD thesis, HEC, Montréal, 1987.
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Haurie, A., Zaccour, G. (2005). S-Adapted Equilibria in Games Played over Event Trees: An Overview. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_23
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DOI: https://doi.org/10.1007/0-8176-4429-6_23
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