Graphon Games with Multiple Equilibria: Analysis and Computation

References

• [1] Akbarpour M, Malladi S, Saberi A (2020) Just a few seeds more: Value of network information for diffusion. Preprint, submitted August 20, http://dx.doi.org/10.2139/ssrn.3062830.Google Scholar
• [2] Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer, Berlin).Google Scholar
• [3] Ash RB, Doleans-Dade CA (2000) Probability and Measure Theory (Academic Press, San Diego).Google Scholar
• [4] Aurell A, Carmona R, Laurière M (2022) Stochastic graphon games: II. The linear-quadratic case. Appl. Math. Optim. 85(3):39.Crossref, Google Scholar
• [5] Aurell A, Carmona R, Dayanıklı G, Laurière M (2022) Finite state graphon games with applications to epidemics. Dynamic Games Appl. 12(1):49–81.Crossref, Google Scholar
• [6] Avella-Medina M, Parise F, Schaub MT, Segarra S (2020) Centrality measures for graphons: Accounting for uncertainty in networks. IEEE Trans. Network Sci. Engrg. 7(1):520–537.Crossref, Google Scholar
• [7] Ballester C, Calvó-Armengol A, Zenou Y (2006) Who’s who in networks. Wanted: The key player. Econometrica 74(5):1403–1417.Crossref, Google Scholar
• [8] Bayraktar E, Chakraborty S, Wu R (2023) Graphon mean field systems. Ann. Appl. Probab. 33(5):3587–3619.Crossref, Google Scholar
• [9] Belgioioso G, Grammatico S (2023) Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games. IEEE Trans. Automatic Control 68(1):140–155.Crossref, Google Scholar
• [10] Bensoussan A, Huang T, Laurière M (2018) Mean field control and mean field game models with several populations. Preprint, submitted October 1, https://arxiv.org/abs/1810.00783.Google Scholar
• [11] Borgs C, Chayes JT, Cohn H, Zhao Y (2019) An Lp theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions. Trans. Amer. Math. Soc. 372(5):3019–3062.Crossref, Google Scholar
• [12] Borgs C, Chayes JT, Lovász L, Sós VT, Vesztergombi K (2008) Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing. Adv. Math. 219(6):1801–1851.Crossref, Google Scholar
• [13] Bramoullé Y, Kranton R (2007) Public goods in networks. J. Econom. Theory 135(1):478–494.Crossref, Google Scholar
• [14] Bramoullé Y, Kranton R, D’Amours M (2014) Strategic interaction and networks. Amer. Econom. Rev. 104(3):898–930.Crossref, Google Scholar
• [15] Caines PE (2021) Mean field games. Baillieul J, Samad T, eds. Encyclopedia of Systems and Control (Springer, Cham, Switzerland), 1197–1202.Crossref, Google Scholar
• [16] Caines PE, Huang M (2021) Graphon mean field games and their equations. SIAM J. Control Optim. 59(6):4373–4399.Crossref, Google Scholar
• [17] Carmona G, Podczeck K (2022) Approximation and characterization of Nash equilibria of large games. Econom. Theory 73(2):679–694.Crossref, Google Scholar
• [18] Carmona R, Cooney DB, Graves CV, Laurière M (2021) Stochastic graphon games: I. The static case. Math. Oper. Res. 47(1):750–778.Link, Google Scholar
• [19] Chien S, Sinclair A (2011) Convergence to approximate Nash equilibria in congestion games. Games Econom. Behav. 71(2):315–327.Crossref, Google Scholar
• [20] Cui K, Koeppl H (2021) Learning graphon mean field games and approximate Nash equilibria. Preprint, submitted November 29, https://doi.org/10.48550/arXiv.2112.01280.Google Scholar
• [21] Dasgupta P, Maskin E (1986) The existence of equilibrium in discontinuous economic games, I: Theory. Rev. Econom. Stud. 53(1):1–26.Crossref, Google Scholar
• [22] Daskalakis C, Papadimitriou CH (2015) Approximate Nash equilibria in anonymous games. J. Econom. Theory 156(C):207–245.Crossref, Google Scholar
• [23] Daskalakis C, Goldberg PW, Papadimitriou CH (2009) The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(1):195–259.Crossref, Google Scholar
• [24] Daskalakis C, Mehta A, Papadimitriou CH (2007) Progress in approximate Nash equilibria. Proc. 8th ACM Conf. Electronic Commerce (San Diego, CA), 355–358.Google Scholar
• [25] Deligkas A, Fearnley J, Savani R, Spirakis P (2017) Computing approximate Nash equilibria in polymatrix games. Algorithmica 77(2):487–514.Crossref, Google Scholar
• [26] Gao S, Caines PE (2019) Spectral representations of graphons in very large network systems control. IEEE 58th Conf. Decision Control (CDC) (Nice, France), 5068–5075.Google Scholar
• [27] Golub B, Jackson MO (2012) Does homophily predict consensus times? Testing a model of network structure via a dynamic process. Rev. Network Econom. 11(3):1–31.Google Scholar
• [28] He W, Sun X, Sun Y (2017) Modeling infinitely many agents. Theoret. Econom. 12(2):771–815.Crossref, Google Scholar
• [29] Housman D (1988) Infinite player noncooperative games and the continuity of the Nash equilibrium correspondence. Math. Oper. Res. 13(3):488–496.Link, Google Scholar
• [30] Jackson MO, Storms EC (2023) Behavioral communities and the atomic structure of networks. Preprint, submitted November 19, https://arxiv.org/abs/1710.04656.Google Scholar
• [31] Jackson MO, Zenou Y (2015) Games on networks. Young HP, Zamir S, eds. Handbook of Game Theory with Economic Applications, vol. 4 (Elsevier, Amsterdam), 95–163.Google Scholar
• [32] Kearns M, Littman ML, Singh S (2015) Graphical models for game theory. Preprint, submitted March 8, https://arxiv.org/abs/1301.2281.Google Scholar
• [33] Khan MA (1985) Equilibrium points of nonatomic games over a nonreflexive Banach space. J. Approximation Theory 43(4):370–376.Crossref, Google Scholar
• [34] Khan MA, Sun Y (2002) Non-cooperative games with many players. Aumann R, Hart S, eds. Handbook of Game Theory with Economic Applications, vol. 3 (Elsevier, Amsterdam), 1761–1808.Google Scholar
• [35] Lasry JM, Lions PL (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• [36] Lovász L (2012) Large Networks and Graph Limits (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• [37] Monderer D, Shapley LS (1996) Potential games. Games Econom. Behav. 14(1):124–143.Crossref, Google Scholar
• [38] Paccagnan D, Gentile B, Parise F, Kamgarpour M, Lygeros J (2019) Nash and Wardrop equilibria in aggregative games with coupling constraints. IEEE Trans. Automatic Control 64(4):1373–1388.Crossref, Google Scholar
• [39] Papadimitriou CH (2001) Algorithms, games, and the internet. Proc. 33rd Annual ACM Sympos. Theory Comput. (Hersonissos, Crete, Greece), 749–753.Google Scholar
• [40] Papadimitriou CH, Roughgarden T (2008) Computing correlated equilibria in multi-player games. J. ACM 55(3):1–29.Crossref, Google Scholar
• [41] Parise F, Ozdaglar A (2021) Analysis and interventions in large network games. Annual Rev. Control Robotics Autonomous Systems 4:455–486.Crossref, Google Scholar
• [42] Parise F, Ozdaglar A (2023) Graphon games: A statistical framework for network games and interventions. Econometrica 91(1):191–225.Crossref, Google Scholar
• [43] Parise F, Grammatico S, Gentile B, Lygeros J (2020) Distributed convergence to Nash equilibria in network and average aggregative games. Automatica 117:108959.Crossref, Google Scholar
• [44] Prisant R, Garin F, Frasca P (2025) Opinion dynamics on signed graphs and graphons. IEEE Trans. Control Network Systems, Early Access October 9, https://doi.org/10.1109/TCNS.2025.3620239.Crossref, Google Scholar
• [45] Rath KP (1992) A direct proof of the existence of pure strategy equilibria in games with a continuum of players. Econom. Theory 2(3):427–433.Crossref, Google Scholar
• [46] Reed M, Simon B (1980) Functional Analysis, Methods of Modern Mathematical Physics, vol. 1 (Academic Press, San Diego).Google Scholar
• [47] Robbins H (1955) A remark on Stirling’s formula. Amer. Math. Monthly 62(1):26–29.Google Scholar
• [48] Rokade K, Parise F (2023) Graphon games with multiple equilibria: Analysis and computation. Proc. 24th ACM Conf. Econom. Comput. (London, UK), 1076.Google Scholar
• [49] Rosen JB (1965) Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33(3):520–534.Crossref, Google Scholar
• [50] Roughgarden T, Tardos E (2004) Bounding the inefficiency of equilibria in nonatomic congestion games. Games Econom. Behav. 47(2):389–403.Crossref, Google Scholar
• [51] Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc. Inst. Civil Engineers 1(3):325–362.Crossref, Google Scholar
• [52] Yang J (2017) A link between sequential semi-anonymous nonatomic games and their large finite counterparts. Internat. J. Game Theory 46(2):383–433.Crossref, Google Scholar
• [53] Yi P, Pavel L (2019) Distributed generalized Nash equilibria computation of monotone games via double-layer preconditioned proximal-point algorithms. IEEE Trans. Control Network Systems 6(1):299–311.Crossref, Google Scholar