Approximations of Nash equilibria

Mathematical Programming

Volumn 117, Issue 1-2, 2009, Pages 223-253

  Gürkan, Gül ^a   Pang, Jong Shi ^b  

^a TILBURG UNIVERSITY   (Netherlands)

^b Rensselaer Polytechnic Institute   (United States)

Author keywords

Competitive capacity expansion under uncertainty; Epiconvergence; Equilibrium models; Stochastic; Variational inequalities

Indexed keywords

OPTIMIZATION; POLYNOMIAL APPROXIMATION; VARIATIONAL TECHNIQUES;

(I ,J) CONDITIONS; (LIQUID + LIQUID) EQUILIBRIUM; CAPACITY EXPANSION; CONVERGENCE (MATHEMATICS); DIRECT APPROACH; NASH EQUILIBRIUM (NE); OPTIMIZ ATION PROBLEMS; OPTIMIZATION APPROACH (OOA); SPRINGER (CO); VARIATIONAL APPROACH (IGC: E6); VARIATIONAL INEQUALITIES;

TELECOMMUNICATION NETWORKS;

EID: 46749133536     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0156-y     Document Type: Article

References (34)

1. Attouch H. (1984). Variational Convergence for Functions and Operators. Pitman Press, Boston
2. Attouch H. and Wets R.J.B. (1981). Approximation and convergence in nonlinear optimization. In: Mangasarian, O.L., Meyer, R.R. and Robinson, S.M. (eds) Nonlinear Programming 4, pp 367-394. Academic, New York
3. Attouch H. and Wets R.J.B. (1983). Convergence des points min/sup et de points fixes. Computes Rendus de l'Académie des Sciences de Paris 296: 657-660
4. Attouch H. and Wets R.J.B. (1983). A convergence theory for saddle functions. Trans. Am. Math. Soc. 280: 1-41
5. Berridge, S., Krawczyk, J.B.: Relaxation algorithms in finding Nash equilibria. Economics Working Paper Archive (1997). [URL: http://econwpa.wustl. edu/eprints/comp/papers/9707/0707002.abs.]
6. Birge J.R. and Louveaux F. (1997). Introduction to Stochastic Programming. Springer, New York
7. Clarke F.H. (1983). Optimization and Nonsmooth Analysis. Wiley, New York
8. Escobar Castro J.F. (2003). Convergencia Variacional en Teoría de Juegos: Existencia, Estabilidad y Aplicaciones a Mercados Eléctricos. Memoria Para Optar a Título de Ingeniero Civil Matemático. Universidad de Chile, Santiago
9. Escobar J.F.: A continuity result for discontinuous games. Department of Economics. Stanford University, Palo Alto, CA (2005, Preprint)
10. Facchinei F. and Pang J.S. (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York
11. Fukushima M. (1992). Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math. Program. 53: 99-110
12. Fukushima M. (1996). Merit functions for variational inequality and complementarity problems. In: Di Pillo, G. and Giannessi, F. (eds) Nonlinear Optimization and Applications., pp 155-170. Plenum, New York
13. Gürkan G., Özge A.Y. and Robinson S.M. (1999). Sample-path solution of stochastic variational inequalities. Math. Program. 84: 313-333
14. Higle J.L. and Sen S. (1996). Stochastic Decomposition: A Statistical Method for Large-Scale Stochastic Linear Programming. Kluwer, Dordrecht
15. Jofré A. and Wets R.J.B. (2002). Continuity properties of Walras equilibrium points. Ann. Oper. Res. 114: 229-243
16. Jofré A. and Wets R.J.B. (2004). Variational bivariate functions: convergence and applications. Manuscript, Department of Mathematics. University of California, Davis, CA
17. Kall P. (1986). Approximation to optimization problems: an elementary review. Math. Oper. Res. 11: 9-18
18. Kall P. and Wallace S.W. (1994). Stochastic Programming. Wiley, Chichester
19. Kolstad C.D. and Mathiesen L. (1991). Computing Nash-Cournot equilibria. Oper. Res. 39: 739-748
20. Krawczyk J.B. (2005). Coupled constraint Nash equilibria in environmental games. Resour. Energy Econ. 27: 157-181
21. Krawczyk J.B. and Uryasev S. (2000). Relaxation algorithms to find Nash equilibria with economic applications. Environ. Model. Assess. 5: 63-73
22. Levy A.B. (2005). Convergence of successive approximation methods with parameter target sets. Math. Oper. Res. 30: 765-784
23. Levy A.B., Poliquin R. and Thibault L. (1995). Partial extensions of Attouch's theorem with applications to proto-derivatives of subgradient mappings. Trans. Am. Math. Soc. 347: 1260-1294
24. Nash J.F. (1951). Non-cooperative games. Ann. Math. 54: 286-295
25. Nikaido H. and Isoda K. (1955). Note on noncooperative convex games. Pac. J. Math. 5(Suppl. 1): 807-815
26. Plambeck E.L., Fu B.R., Robinson S.M. and Suri R. (1996). Sample-path optimization of convex stochastic performance functions. Math. Program. 75: 137-176
27. Poliquin R. (1992). An extension of Attouch's theorem and its applicataion to second-order epi-differentiation of convexly composite functions. Trans. Am. Math. Soc. 332: 861-874
28. Robinson S.M. (1996). Analysis of sample-path optimization. Math. Oper. Res. 21: 513-528
29. Rockafellar R.T. and Wets R.J.-B. (1998). Variational Analysis. Springer, Berlin
30. Rosen J.B. (1965). Existence and uniqueness for concave n-person games. Econometrica 33: 520-534
31. Ruszczyński, A., Shapiro, A. (eds.) Stochastic Programming. Handbook in Operations Research and Management Science, vol. 10. North-Holland, The Netherlands (2003)
32. Shapiro, A., Xu, H.: Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation. (URL: http://www.optimization-online.org/DB_HTML/2005/01/1046.html) (revised June 2005)
33. Uryasev S. and Rubinstein R.T. (1994). On relaxation algorithms in computation of Nash equilibria. IEEE Trans. Automat. Control 39: 1263-1267
34. Wets R.J.B. (1980). Convergence of convex functions, variational inequalities and convex optimization problems. In: Cottle, R.W., Gianessi, F., and Lions, J.L. (eds) Variational Inequalities and Complementarity Problems., pp 375-403. Wiley, Chichester