Stability for Nash Equilibrium Problems

References

• [1] Aubin JP (1984) Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. 9(1):87–111.Link, Google Scholar
• [2] Aubin JP (1998) Optima and Equilibria: An Introduction to Nonlinear Analysis, Graduate Texts in Mathematics series, vol. 140 (Springer, Berlin).Google Scholar
• [3] Berge C (1963) Topological Spaces (Macmillan, New York).Google Scholar
• [4] Bonnans JF, Ramírez CH (2005) Perturbation analysis of second-order cone programming problems. Math. Programming 104(2):205–227.Crossref, Google Scholar
• [5] Cho YJ, Chen YQ (2006) Topological Degree Theory and Applications (Chapman and Hall/CRC, Boca Raton, FL).Crossref, Google Scholar
• [6] Contreras J, Klusch M, Krawczyk JB (2004) Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets. IEEE Trans. Power Systems 19(1):195–206.Crossref, Google Scholar
• [7] Ding C, Sun D, Zhang L (2017) Characterization of the robust isolated calmness for a class of conic programming problems. SIAM J. Optim. 27(1):67–90.Crossref, Google Scholar
• [8] Dontchev AL, Rockafellar RT (1996) Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim. 6(4):1087–1105.Crossref, Google Scholar
• [9] Dontchev AL, Rockafellar RT (1997) Characterizations of Lipschitzian stability in nonlinear programming. Fiacco AV, ed. Mathematical Programming with Data Perturbations (Marcel Dekker, New York), 65–82.Google Scholar
• [10] Dontchev AL, Rockafellar RT (2009) Implicit Functions and Solution Mappings, Springer Series in Operations Research and Financial Engineering, vol. 543 (Springer, New York).Crossref, Google Scholar
• [11] Facchinei F, Kanzow C (2010) Generalized Nash equilibrium problems. Ann. Oper. Res. 175(1):177–211.Crossref, Google Scholar
• [12] Facchinei F, Pang JS (2003) Finite-Dimensional Variational Inequalities and Complementarity Problems, Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. 1 (Springer, New York).Google Scholar
• [13] Farnia F, Ozdaglar A (2020) Do GANs always have Nash equilibria? Internat. Conf. Machine Learn. (PMLR, Cambridge, MA), 3029–3039.Google Scholar
• [14] Fiacco AV, McCormick GP (1990) Nonlinear Programming: Sequential Unconstrained Minimization Techniques (SIAM, Philadelphia).Crossref, Google Scholar
• [15] Gibbons R (1992) Game Theory for Applied Economists (Princeton University Press, Princeton, NJ).Google Scholar
• [16] Klatte D, Kummer B (2002) Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications, Nonconvex Optimization and Its Applications series, vol. 60 (Springer, New York).Google Scholar
• [17] Kojima M (1978) Studies on piecewise-linear approximations of piecewise-C1 mappings in fixed points and complementarity theory. Math. Oper. Res. 3(1):17–36.Link, Google Scholar
• [18] Kojima M, Okada A, Shindoh S (1985) Strongly stable equilibrium points of N-person noncooperative games. Math. Oper. Res. 10(4):650–663.Link, Google Scholar
• [19] Kyparisis J (1985) On uniqueness of Kuhn-Tucker multipliers in nonlinear programming. Math. Programming 32(2):242–246.Crossref, Google Scholar
• [20] Mordukhovich BS, Outrata JV (2007) Coderivative analysis of quasi-variational inequalities with applications to stability and optimization. SIAM J. Optim. 18(2):389–412.Crossref, Google Scholar
• [21] Mordukhovich BS, Outrata JV, Ramírez C H (2015) Graphical derivatives and stability analysis for parameterized equilibria with conic constraints. Set-Valued Var. Anal. 23(4):687–704.Crossref, Google Scholar
• [22] Myerson RB (2013) Game Theory (Harvard University Press, Cambridge, MA).Crossref, Google Scholar
• [23] Nash JF (1951) Non-cooperative games. Ann. Math. 54(2):286–295.Crossref, Google Scholar
• [24] Nocedal J, Wright SJ (1999) Numerical Optimization (Springer, New York).Crossref, Google Scholar
• [25] Palomar DP, Eldar YC (2010) Convex Optimization in Signal Processing and Communications (Cambridge University Press, Cambridge, UK).Google Scholar
• [26] Robinson SM (1975) Stability theory for systems of inequalities. Part I: Linear systems. SIAM J. Numer. Anal. 12(5):754–769.Crossref, Google Scholar
• [27] Robinson SM (1980) Strongly regular generalized equations. Math. Oper. Res. 5(1):43–62.Link, Google Scholar
• [28] Robinson SM (1982) Generalized equations and their solutions, part II: Applications to nonlinear programming. Guignard M, ed. Optimality and Stability in Mathematical Programming (Springer, Berlin), 200–221.Crossref, Google Scholar
• [29] Rockafellar RT (2018) Variational analysis of Nash equilibrium. Vietnam J. Math. 46(1):73–85.Crossref, Google Scholar
• [30] Rockafellar RT (2024) Generalized Nash equilibrium from a robustness perspective in variational analysis. Set-Valued Var. Anal. 32(2):19.Crossref, Google Scholar
• [31] Rockafellar RT, Wets RJB (1998) Variational Analysis, Grundlehren der mathematischen Wissenschaften, vol. 317 (Springer, Berlin).Crossref, Google Scholar
• [32] Young P, Zamir S (2014) Handbook of Game Theory, Handbook of Game Theory with Economic Applications, vol. 4 (Elsevier, Amsterdam).Google Scholar