Relaxation algorithms to find Nash equilibria with economic applications
作者： Jacek B. Krawczyk , Stanislav Uryasev
关键词: Computational economics 、 Mathematical optimization 、 Relaxation (approximation) 、 Algorithm 、 Convergence (routing) 、 Range (mathematics) 、 Relaxation algorithm 、 Mathematics 、 Stochastic game 、 Nonlinear system 、 Nash equilibrium
摘要: Recent theoretical studies have shown that a relaxation algorithm can be used to find noncooperative equilibria of synchronous infinite games with nonlinear payoff functions and coupled constraints. In this study, we introduce an improvement the algorithm, such as steepest-descent step-size control, for which convergence is proved. The then tested on several economic applications. particular, River Basin Pollution problem considered where environmental constraints are crucial relevant model definition. Numerical runs demonstrate fast wide range parameters.
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sci-hub.se 参考文章(16)
Jean Pierre Aubin, Mathematical methods of game and economic theory ,(1979)
Anna Nagurney, Network Economics: A Variational Inequality Approach ,(1992)
Jong-Shi Pang, Michael C. Ferris, Complementarity and variational problems : state of the art Society for Industrial and Applied Mathematics. ,(1997)
G. P. Papavassilopoulos, Iterative Techniques for the Nash Solution in Quadratic Games with Unknown Parameters SIAM Journal on Control and Optimization. ,vol. 24, pp. 821- 834 ,(1986) , 10.1137/0324052
J. B. Rosen, Existence and uniqueness of equilibrium points for concave n-person games Econometrica. ,vol. 33, pp. 251- 251 ,(1965) , 10.2307/1911749
W.David Montgomery, Markets in licenses and efficient pollution control programs Journal of Economic Theory. ,vol. 5, pp. 395- 418 ,(1972) , 10.1016/0022-0531(72)90049-X
Tamer Başar, Relaxation techniques and asynchronous algorithms for on-line computation of non-cooperative equilibria Journal of Economic Dynamics and Control. ,vol. 11, pp. 531- 549 ,(1987) , 10.1016/S0165-1889(87)80006-4
Krzysztof C. Kiwiel, Andrzej Ruszcayǹski, N. Z. Shor, Minimization methods for non-differentiable functions ,(1985)
S.P. Uryas'ev, On the anti-monotonicity of differential mappings connected with general equilibrium problem Optimization. ,vol. 19, pp. 693- 709 ,(1988) , 10.1080/02331938808843385
Shu Li, Tamer Başar, Distributed algorithms for the computation of noncooperative equilibria Automatica. ,vol. 23, pp. 523- 533 ,(1987) , 10.1016/0005-1098(87)90081-1