# zbMATH — the first resource for mathematics

Computing all solutions of Nash equilibrium problems with discrete strategy sets. (English) Zbl 1414.91017

##### MSC:
 91A10 Noncooperative games 91A06 $$n$$-person games, $$n>2$$ 91-04 Software, source code, etc. for problems pertaining to game theory, economics, and finance 90C10 Integer programming
PATH Solver
Full Text:
##### References:
 [1] T. Basar and G. Olsder, Dynamic Noncooperative Game Theory, 2nd ed., SIAM, Philadelphia, PA, 1999. · Zbl 0946.91001 [2] P. Belotti, C. Kirches, S. Leyffer, J. Linderoth, J. Luedtke, and A. Mahajan, Mixed-integer nonlinear optimization, Acta Numer., 22 (2013), pp. 1–131. · Zbl 1291.65172 [3] P. Belotti, J. Lee, L. Liberti, F. Margot, and A. Wächter, Branching and bounds tightening techniques for non-convex MINLP, Optim. Methods Softw., 24 (2009), pp. 597–634. · Zbl 1179.90237 [4] S. Bikhchandani and J. Mamer, Competitive equilibrium in an exchange economy with indivisibilities, J. Econ. Theory, 74 (1997), pp. 385–413. · Zbl 0887.90051 [5] R. Cottle, J.-S. Pang, and R. Stone, The Linear Complementarity Problem, Academic Press, Boston, 1992. · Zbl 0757.90078 [6] S. Dirkse and M. Ferris, The path solver: a nommonotone stabilization scheme for mixed complementarity problems, Optim. Methods Softw., 5 (1995), pp. 123–156. [7] A. Dreves, F. Facchinei, C. Kanzow, and S. Sagratella, On the solution of the KKT conditions of generalized Nash equilibrium problems, SIAM J. Optim., 21 (2011), pp. 1082–1108. · Zbl 1230.90176 [8] A. Dreves and C. Kanzow, Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems, Comput. Optim. Appl., 50 (2011), pp. 23–48. · Zbl 1227.90040 [9] A. Dreves, C. Kanzow, and O. Stein, Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems, J. Global Optim., 53 (2012), pp. 587–614. · Zbl 1281.90055 [10] A. Fabrikant, C. Papadimitriou, and K. Talwar, The complexity of pure Nash equilibria, in Proceedings of the 36th Annual ACM Symposium on Theory of Computing, ACM, 2004, pp. 604–612. · Zbl 1192.91042 [11] F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems, Ann. Oper. Res., 175 (2010), pp. 177–211. · Zbl 1185.91016 [12] F. Facchinei, C. Kanzow, and S. Sagratella, Solving quasi-variational inequalities via their KKT conditions, Math. Program., 144 (2014), pp. 369–412. · Zbl 1293.65100 [13] F. Facchinei and L. Lampariello, Partial penalization for the solution of generalized Nash equilibrium problems, J. Global Optim., 50 (2011), pp. 39–57. · Zbl 1236.91015 [14] F. Facchinei, L. Lampariello, and S. Sagratella, Recent advancements in the numerical solution of generalized Nash equilibrium problems, Quad. Mat. (Volume in ricordo di Marco D’Apuzzo) 27 (2012), pp. 137–174. [15] F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer, New York, 2003. · Zbl 1062.90002 [16] F. Facchinei, V. Piccialli, and M. Sciandrone, Decomposition algorithms for generalized potential games, Comput. Optim. Appl., 50 (2011), pp. 237–262. · Zbl 1237.91017 [17] F. Facchinei and S. Sagratella, On the computation of all solutions of jointly convex generalized Nash equilibrium problems, Optim. Lett., 5 (2011), pp. 531–547. · Zbl 1259.91009 [18] M. Ferris and T. Munson, Interfaces to PATH 3.0: Design, implementation and usage, Comput. Optim. Appl., 12 (1999), pp. 207–227. · Zbl 1040.90549 [19] S. Gabriel, A. Conejo, C. Ruiz, and S. Siddiqui, Solving discretely constrained, mixed linear complementarity problems with applications in energy, Comput. Oper. Res., 40 (2013), pp. 1339–1350. · Zbl 1352.90097 [20] S. Gabriel, S. Siddiqui, A. Conejo, and C. Ruiz, Solving discretely-constrained Nash–Cournot games with an application to power markets, Netw. Spat. Econ., 13 (2013), pp. 307–326. · Zbl 1339.91027 [21] G. V. D. Laan, D. Talman, and Z. Yang, Computing integral solutions of complementarity problems, Discrete Optim., 4 (2007), pp. 315–321. · Zbl 1153.90552 [22] K. Nabetani, P. Tseng, and M. Fukushima, Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints, Comput. Optim. Appl., 48 (2011), pp. 423–452. · Zbl 1220.90136 [23] J. F. Nash, Equilibrium points in n-person games, Proc. Natl. Acad. Sci. USA, 36 (1950), pp. 48–49. · Zbl 0036.01104 [24] J. F. Nash, Non-cooperative games, Ann. Math., 54 (1951), pp. 286–295. · Zbl 0045.08202 [25] I. Nowak, Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming, International, Series of Numerical Mathematics, 152, Springer, Basel, 2006. [26] J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games, Comput. Manag. Sci., 2 (2009), pp. 21–56. · Zbl 1115.90059 [27] B. V. Stengel, Computing equilibria for two-person games, in Handbook of Game Theory with Economic Applications, vol. 3, R. J. Aumann and S. Mat, eds., Elsevier, Amsterdam, 2002, pp. 1723–1759. [28] M. Tawarmalani and N. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Nonconvex Optimization and Its Applications, 65, Springer, Dordrecht, 2002. · Zbl 1031.90022 [29] J. Tirole, The Theory of Industrial Organization, MIT Press, Cambridge, MA, 1988. [30] D. Topkis, Supermodularity and Complementarity, Princeton University Press, Princeton, NJ, 1998. [31] Z. Yang, On the solutions of discrete nonlinear complementarity and related problems, Math. Oper. Res., 33 (2008), pp. 976–990. · Zbl 1218.90198
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.