Approximate Nash Equilibria in Large Nonconvex Aggregative Games
References
- [1] (1976) Estimates of the duality gap in nonconvex optimization. Math. Oper. Res. 1(3):225–245.Link, Google Scholar
- [2] (2016) Oligopoly and cost sharing in economics with public goods. Internat. Econom. Rev. 57(2):487–505.Crossref, Google Scholar
- [3] (1979) Convexification procedures and decomposition methods for nonconvex optimization problems. J. Optim. Theory Appl. 29(2):169–197.Crossref, Google Scholar
- [4] (1996) Constrained-Optimization and Lagrangian Multiplier Methods (Athena Scientific, Belmont, MA).Google Scholar
- [5] (2009) Convex Optimization Theory (Athena Scientific, Belmont, MA).Google Scholar
- [6] (1982) Estimates of the duality gap for large-scale separable nonconvex optimization problems. 21st IEEE Conf. Decision Control (IEEE, Orlando, FL), 782–785.Google Scholar
- [7] (1983) Optimal short-term scheduling of large-scale power systems. IEEE Trans. Automatic Control 28(1):1–11.Crossref, Google Scholar
- [8] (2020) Duality gap estimation via a refined Shapley–Folkman lemma. SIAM J. Optim. 30(2):1094–1118.Crossref, Google Scholar
- [9] (1994) Comparative statics for aggregative games: The strong concavity case. Math. Soc. Sci. 28(3):151–165.Crossref, Google Scholar
- [10] (1980) Traffic equilibrium and variational inequalities. Transportation Sci. 14(1):42–54.Link, Google Scholar
- [11] (1992) A general analysis of rent-seeking games. Public Choice 73(3):335–350.Crossref, Google Scholar
- [12] (1999) Convex Analysis and Variational Problems (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
- [13] (2003) Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer-Verlag, New York).Google Scholar
- [14] (2019) Blessing of massive scale: Spatial graphical model estimation with a total cardinality constraint approach. Math. Programming 176(1–2):175–205.Crossref, Google Scholar
- [15] (2018) Strategic decentralization and the provision of global public goods. J. Environ. Econom. Management 92:537–558.Crossref, Google Scholar
- [16] (1993) Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods (Springer-Verlag, Berlin/Heidelberg).Crossref, Google Scholar
- [17] (1998) Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- [18] (2018) Real-time enforcement of local energy market transactions respecting distribution grid constraints. Popovski P, ed. 2018 IEEE Internat. Conf. Comm. Control Comput. Tech. Smart Grids (IEEE, Aalborg, Denmark), 1–7.Google Scholar
- [19] (2021) New insights from the Shapley-Folkman lemma on dispatchable demand in energy markets. IEEE Trans. Power Systems 36(5):4028–4041.Crossref, Google Scholar
- [20] (2017) Demand response in the smart grid: The impact of consumers temporal preferences. Lehnert R, Speh R, eds. 2017 IEEE Internat. Conf. Smart Grid Comm. (IEEE, Dresden, Germany), 540–545.Google Scholar
- [21] (2021) Efficient estimation of equilibria in large aggregative games with coupling constraints. IEEE Trans. Automatic Control 66(6):2762–2769.Crossref, Google Scholar
- [22] (2010) Aggregative games and best-reply potentials. Econom. Theory 43(1):45–66.Crossref, Google Scholar
- [23] (1941) A generalization of Brouwer’s fixed point theorem. Duke Math. J. 8(3):457–459.Crossref, Google Scholar
- [24] (2019) An approximate Shapley-Folkman theorem. Preprint, https://arxiv.org/abs/1712.08559.Google Scholar
- [25] (1982) Solution of large-scale optimal unit commitment problems. IEEE Trans. Power Apparatus Systems PAS-101(1):79–86.Crossref, Google Scholar
- [26] (1997) Atomic resource sharing in noncooperative networks. Proc. INFOCOM ’97, vol. 3 (IEEE, Kobe, Japan), 1006–1013.Google Scholar
- [27] (2007) Traffic equilibrium. Laporte G, Barnhart C, eds. Transportation, vol. 14 (Elsevier), 623–713.Google Scholar
- [28] (2006) Network flow problems and congestion games: Complexity and approximation results. Unpublished PhD dissertation, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
- [29] (1982) A mathematical programming approach for determining oligopolistic market equilibrium. Math. Programming 24(1):92–106.Crossref, Google Scholar
- [30] (1993) A theory of voting equilibria. Amer. Political Sci. Rev. 87(1):102–114.Crossref, Google Scholar
- [31] (1993) Competitive routing in multiuser communication networks. IEEE/ACM Trans. Networks 1(5):510–521.Crossref, Google Scholar
- [32] (2016) On aggregative and mean field games with applications to electricity markets. 2016 Eur. Control Conf. (IEEE, Aalborg, Denmark), 196–201.Google Scholar
- [33] (2019) Nash and Wardrop equilibria in aggregative games with coupling constraints. IEEE Trans. Automatic Control 64(4):1373–1388.Crossref, Google Scholar
- [34] (1983) A strategic calculus of voting. Public Choice 41(1):7–53.Crossref, Google Scholar
- [35] (1986) On the duality gap in nonconvex optimization. Math. Oper. Res. 11(1):30–35.Link, Google Scholar
- [36] (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3):520–534.Crossref, Google Scholar
- [37] (1973) A class of games possessing pure-strategy Nash equilibria. Internat. J. Game Theory 2(1):65–67.Crossref, Google Scholar
- [38] (2016) Computing all solutions of Nash equilibrium problems with discrete strategy sets. SIAM J. Optim. 26(4):2190–2218.Crossref, Google Scholar
- [39] (2014) Real and complex monotone communication games. IEEE Trans. Inform. Theory 60(7):4197–4231.Crossref, Google Scholar
- [40] (1970) Preispolitik der Mehrproduktenunternehmung in der Statischen Theorie (Springer Verlag, Berlin).Crossref, Google Scholar
- [41] (1969) Quasi-equilibria in markets with non-convex preferences. Econometrica 37(1):25–38.Crossref, Google Scholar
- [42] (2011) On the existence of pure strategy Nash equilibria in integer–splittable weighted congestion games. Algorithmic Game Theory (Springer, Berlin/Heidelberg), 236–253.Crossref, Google Scholar
- [43] (2016) Bounding duality gap for separable problems with linear constraints. Comput. Optim. Appl. 64(2):355–378.Crossref, Google Scholar
- [44] (2014) Large scale mixed-integer optimization: A solution method with supply chain applications. 22nd Mediterranean Conf. Control Automation (IEEE, Paleromo, Italy), 804–809.Google Scholar
- [45] (2016) A decomposition method for large scale MILPs, with performance guarantees and a power system application. Automatica 67:144–156.Crossref, Google Scholar
- [46] (2017) Vanishing price of decentralization in large coordinative nonconvex optimization. SIAM J. Optim. 27(3):1977–2009.Crossref, Google Scholar
- [47] (2013) A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion. SIAM J. Imaging Sci. 6(3):1758–1789.Crossref, Google Scholar
- [48] (2006) Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Trans. Comm. 54(7):1310–1322.Crossref, Google Scholar

