Solving quadratic multi-leader-follower games by smoothing the follower's best response

References

• E. Allevi, D. Aussel, and R. Riccardi, On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity, J. Global Optim. 70(2) (2018), pp. 329–346. ISSN 1573–2916.
   Web of Science ®Google Scholar
• D. Aussel and A. Svensson, Some remarks about existence of equilibria, and the validity of the epcc reformulation for multi-leader-follower games, J. Nonlinear Convex Anal. 19(7) (2018), pp. 1141–1162.
   Web of Science ®Google Scholar
• D. Aussel, M. Cervinka, and M. Marechal, Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions, RAIRO-Oper. Res. 50(1) (2016), pp. 19–38.
   Web of Science ®Google Scholar
• D. Aussel, P. Bendotti, and M. Pištěk, Nash equilibrium in a pay-as-bid electricity market: Part 1–existence and characterization, Optimization 66(6) (2017a), pp. 1013–1025.
   Web of Science ®Google Scholar
• D. Aussel, P. Bendotti, and M. Pištěk, Nash equilibrium in a pay-as-bid electricity market: Part 2–best response of a producer, Optimization 66(6) (2017b), pp. 1027–1053.
   Web of Science ®Google Scholar
• A.M. Bagirov, L. Jin, N. Karmitsa, A. AlNuaimat, and N. Sultanova, Subgradient method for nonconvex nonsmooth optimization, J. Optim. Theory Appl. 157(2) (2013), pp. 416–435. ISSN 1573–2878.
   Web of Science ®Google Scholar
• V. DeMiguel and H. Xu, A stochastic multiple-leader stackelberg model: Analysis, computation, and application, Oper. Res. 57(5) (2009), pp. 1220–1235. doi:10.1287/opre.1080.0686.
   Web of Science ®Google Scholar
• S.P. Dirkse and M.C. Ferris, The path solver: A nommonotone stabilization scheme for mixed complementarity problems, Optim. Methods Softw. 5(2) (1995), pp. 123–156. doi:10.1080/10556789508805606.
   Google Scholar
• F. Facchinei and J. Pang, Finite-dimensional variational inequalities and complementarity problems. Springer Series in Operations Research and Financial Engineering. Springer New York, 2007.
   Google Scholar
• M.C. Ferris and T.S. Munson, Interfaces to PATH 3.0: Design, Implementation and Usage In Computational Optimization, Springer US, 1999, pp. 207–227. doi:10.1007/978-1-4615-5197-3_11.
   Google Scholar
• R. Henrion, J. Outrata, and T. Surowiec, Analysis of m-stationary points to an epec modeling oligopolistic competition in an electricity spot market, ESAIM: Control Optim. Calc. Var. 18(2) (2012), pp. 295–317.
   Web of Science ®Google Scholar
• M. Hu and M. Fukushima, Existence, uniqueness, and computation of robust nash equilibria in a class of multi-leader-follower games, SIAM J. Optim. 23(2) (2013), pp. 894–916.
   Web of Science ®Google Scholar
• X. Hu and D. Ralph, Using epecs to model bilevel games in restructured electricity markets with locational prices, Oper. Res. 55(5) (2007), pp. 809–827.
   Web of Science ®Google Scholar
• R. Janin, Directional Derivative of the Marginal Function in Nonlinear Programming, Springer Berlin Heidelberg, Berlin, Heidelberg, 1984), pp. 110–126. doi:10.1007/BFb0121214.
   Google Scholar
• Y. Kim and M.C. Ferris, Solving equilibrium problems using extended mathematical programming, Math. Program. Comput. 11(3) (2019), pp. 457–501. doi:10.1007/s12532-019-00156-4.
   Web of Science ®Google Scholar
• A. Koh and S. Shepherd, Tolling, collusion and equilibrium problems with equilibrium constraints, 2010. ISSN 1825–3997.
   Google Scholar
• A.A. Kulkarni and U.V. Shanbhag, A shared-constraint approach to multi-leader multi-follower games, Set-Valued Var. Anal. 22(4) (2014), pp. 691–720. doi:10.1007/s11228-014-0292-5.
   Web of Science ®Google Scholar
• A.A. Kulkarni and U.V. Shanbhag, An existence result for hierarchical stackelberg v/s stackelberg games, IEEE Trans. Automat. Control 60(12) (2015), pp. 3379–3384. doi:10.1109/tac.2015.2423891.
   Web of Science ®Google Scholar
• S. Leyffer and T. Munson, Solving multi-leader-common-follower games, Optim. Methods Softw. 25(4) (2010), pp. 601–623.
   Web of Science ®Google Scholar
• D. Monderer and L.S. Shapley, Potential games, Games. Econ. Behav. 14(1) (1996), pp. 124–143. ISSN 0899–8256.
   Web of Science ®Google Scholar
• H. Nikaidô and K. Isoda, Note on non-cooperative convex game, Pacific J. Math. 5(5) (1955), pp. 807–815.
   Google Scholar
• J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized nash equilibria, and multi-leader-follower games, Comput. Manage. Sci. 2(1) (2005), pp. 21–56. ISSN 1619–6988.
   Google Scholar
• L. Qi and J. Sun, A nonsmooth version of newton's method, Math. Program. 58(1) (1993), pp. 353–367. ISSN 1436–4646.
   Web of Science ®Google Scholar
• H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity, Math. Oper. Res. 25(1) (2000), pp. 1–22. ISSN 0364765X, 15265471.
   Web of Science ®Google Scholar
• H.D. Sherali, A multiple leader stackelberg model and analysis, Oper. Res. 32(2) (1984), pp. 390–404.
   Web of Science ®Google Scholar
• S. Steffensen and A. Thünen, An explicit nash equilibrium to a multi-leader-follower game, In PAMM-Proc. Appl. Math. Mech. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2019.
   Google Scholar
• S. Steffensen and M. Ulbrich, A new relaxation scheme for mathematical programs with equilibrium constraints, SIAM. J. Optim. 20(5) (2010), pp. 2504–2539.
   Web of Science ®Google Scholar
• C.-L. Su, A sncp method for solving equilibrium problems with equilibrium constraints, Comput. Econom. Finance 150 (2005).
   Google Scholar
• C.-L. Su, Analysis on the forward market equilibrium model, Oper. Res. Lett. 35(1) (2007), pp. 74–82. doi:10.1016/j.orl.2006.01.006.
   Web of Science ®Google Scholar
• J.H. Wang, D.M. Chiu, and J.C.S. Lui, A game-theoretic analysis of the implications of overlay network traffic on ips peering, Comput. Netw. 52 (2008), pp. 2961–2974.
   Web of Science ®Google Scholar