Network games; adaptations to Nash-Cournot equilibrium

Annals of Operations Research

Volumn 64, Issue , 1996, Pages 179-195

  Flåm, Sjur Didrik ^a   Horvath, Charles ^b  

^a UNIVERSITY OF BERGEN   (Norway)

^b UNIVERSITÉ DE PERPIGNAN   (France)

Author keywords

Nash equilibrium; Network flows; Noncooperative games; Stochastic approximation; Subgradient projection

Indexed keywords

EID: 0011423129     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/BF02187645     Document Type: Article

References (29)

1. M. Aoki, On some price adjustment schemes, Ann. Econ. Soc. Measure 3, 1974, 95-115.
2. W.B. Arthur, Yu.M. Ermol'ev and Yu.M. Kaniovski, Non-linear urn processes: Asymptotic behavior and applications, IIASA, Working Paper 85, 1987.
3. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhaüser, Basel, 1990.
4. R.J. Aumann and S. Hart (eds.), Handbook of Game Theory, vol. I, North Holland, Amsterdam, 1992.
5. O.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation, Prentice-Hall International, London, 1989.
6. D.P. Bertsekas, P.A. Hosein and P. Tseng, Relaxation methods for network flow problems with convex arc costs, SIAM J. Control and Optim. 25,1987, 1219-1243.
7. A. Benveniste, M. Métivier and P. Priouret, Adaptive Algorithms and Stochastic Approximations, Springer, Berlin, 1990.
8. K. Binmore and P. Dasgupta, Game theory: A survey, in Economic Organizations and Games, K. Binmore and P. Dasgupta, eds., Basil Blackwell, Oxford, 1986, pp. 1-45.
9. A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, 1838;
10. English edition: Researches into the Mathematical Principles of the Theory of Wealth, Macmillan, New York, 1897.
11. S. Dafermos and A. Nagurney, Oligopolistic and competitive behavior of spatially separated markets, Regional Science and Urban Economics 17, 1987, 245-254.
12. Yu.M. Ermol'ev and S.P. Uryas'ev, Nash equilibrium in n-person games (in Russian), Kibernetika 3, 1982, 85-88.
13. Yu.M. Ermol'ev, Stochastic quasigradient methods, in Numerical Techniques for Stochastic Optimization, Yu. Ermol'ev and R.J-B Wets, eds., Springer, Berlin, 1989, pp. 141-185.
14. D. Fudenberg and D.M. Kreps, Learning mixed equilibria, Games and Economic Behavior 5, 1993, 320-367.
15. M. Gondran and M. Minoux, Graphes et Algorithmes, Editions Eyrolles, Paris, 1990.
16. P.T. Harker, Alternative models of spatial competition, Operations Research 34, 1986, 410-425.
17. P.T. Harker and J.-S. Pang, Finite-dimensional variational inequalities and nonlinear complementarity problems: A survey of theory, algorithms and applications, Mathematical Programming 48, 1990, 161-220.
18. A. Haurie and P. Marcotte, On the relationship between Nash-Cournot and Wardrop equilibria, Networks 15, 1985, 295-308.
19. H.J. Kushner and D.S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems, Applied Math. Sciences 26, Springer, Berlin, 1978.
20. A. Marcet and T. J. Sargent, Convergence of least squares learning mechanism in self-referential linear stochastic models, J. Economic Theory 48, 1989, 337-368.
21. F.H. Murphy, H.D. Sherali and A.L. Soyster, A mathematical programming approach for determining oligopolistic market equilibrium, Mathematical Programming 24, 1982, 92-106.
22. A. Nagumey, Network Economics, A Variational Inequality Approach, Kluwer Academic, Dordrecht, 1993.
23. J.F. Nash, Noncooperative games, Annals of Mathematics 54, 1951, 286-298.
24. B.T. Polyak, Introduction to Optimization, Optimization Software, Inc., New York, 1987.
25. H. Robbins and D. Siegmund, A convergence theorem for nonnegative almost surmartingales and some applications, in Optimizing Methods in Statistics, J. Rustagi, ed., Academic Press, New York, 1971, pp. 235-257.
26. R.T. Rockafellar, Convex Analysis, Princeton University Press, NJ, 1970.
27. R.T. Rockafellar, Network Flows and Monotropic Optimization, Wiley, New York, 1984.
28. J.B. Rosen, Existence and uniqueness of equilibrium point for concave N-person games, Econometrica 33, 1965, 520-534.
29. J. Tirole, The Theory of Industrial Organization, MIT Press, Cambridge, 1988.