Robust nash equilibria in N-person non-cooperative games: Uniqueness and reformulation

Pacific Journal of Optimization

Volumn 5, Issue 2, 2009, Pages 237-259

  Nishimura, Ryoichi ^a   Hayashi, Shunsuke ^a   Fukushima, Masao ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Complementarity problem; Incomplete information; N person non cooperative game; Robust Nash equilibrium; Robust optimization

Indexed keywords

EID: 78049438822     PISSN: 13489151     EISSN: 13498169     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. M. Aghassi and D. Bertsimas, Robust game theory, Math. Program. 107 (2006) 231-273.
2. F. Alizadeh and D. Goldfarb, Second-order cone programming, Math. Program. 95 (2003) 3-51.
3. J.-P. Aubin, Mathematical Methods of Game and Economic Theory, North-Holland Publishing Company, Amsterdam, 1979.
4. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, 1990.
5. A. Ben-Tal and A. Nemirovski, Robust convex optimization, Math. Oper. Res. 23 (1998) 769-805.
6. A. Ben-Tal and A. Nemirovski, Robust solutions of uncertain linear programs, Oper. Res. Lett. 25 (1999) 1-13.
7. A. Ben-Tal and A. Nemirovski, Selected topics in robust convex optimization, Math. Program. 112 (2008) 125-158.
8. D.P. Bertsekas, Convex Analysis and Optimization, Athena Scientific, 2003.
9. L. ElGhaoui and H. Lebret, Robust solutions to least-squares problem with uncertain data, SIAM J. Matrix Anal. Appl. 18 (1997) 1035-1064.
10. F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer-Verlag, New York, 2003.
11. S.C. Fang and E.L. Peterson, Generalized variational inequalities, J. Optim. Theory Appl. 38 (1982) 363-383.
12. D. Fudenberg and J. Tirole, Game Theory, The MIT Press, 1991.
13. M. Fukushima, Z.-Q. Luo, and P. Tseng, Smoothing functions for second-order cone complementarity problems, SIAM J. Optim. 12 (2001) 436-460.
14. J. Harsanyi, Games with incomplete information played by 'Bayesian' players, Part I, Manag. Sci. 14 (1967) 159-182.
15. J. Harsanyi, Games with incomplete information played by 'Bayesian' players, Part II, Manag. Sci. 14 (1968) 320-334.
16. J. Harsanyi, Games with incomplete information played by 'Bayesian' players, Part III, Manag. Sci. 14 (1968) 486-502.
17. S. Hayashi, N. Yamashita, and M. Fukushima, A combined smoothing and regularization method for monotone second-order cone complementarity problems, SIAM J. Optim. 175 (2005) 335-353.
18. S. Hayashi, N. Yamashita, and M. Fukushima, Robust Nash equilibria and second-order cone complementarity problems, J. Nonlinear Convex Anal. 6 (2005) 283-296.
19. R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
20. R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
21. R.B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1991.
22. J. Nash, Equilibrium points in N-person games, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 36 (1950) 48-49.
23. J. Nash, Non-cooperative games, Ann. of Math. 54 (1951) 286-295.
24. J.B. Rosen, Existence and uniqueness of equilibrium points for concave N-persons games, Econometrica 33 (1965) 520-534.