Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 35 | |
Number of page(s) | 59 | |
DOI | https://doi.org/10.1051/cocv/2024023 | |
Published online | 22 April 2024 |
- J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 2nd revised edn. Princeton University Press (1947). [Google Scholar]
- T. Killingback and M. Doebeli, Spatial evolutionary game theory: hawks and doves revisited. Proc. Biol. Sci. 263 (1996) 1135–1144. [CrossRef] [Google Scholar]
- J. Ghaderi and R. Srikant, Opinion dynamics in social networks: a local interaction game with stubborn agents, in 2013 American Control Conference. IEEE (2013) 1982–1987. [CrossRef] [Google Scholar]
- M. Huang R.P. Malhamé and P.E. Caines, Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inform. Syst. (2006). [Google Scholar]
- J.M. Lasry and P.L. Lions, Mean field games. Jap. J. Math. 2 (2007) 229–260. [CrossRef] [Google Scholar]
- Y. Achdou, J. Han and J.M. Lasry, et al., Income and wealth distribution in macroeconomics: a continuous-time approach. Rev. Econ. Stud. 89 (2022) 45–86. [CrossRef] [MathSciNet] [Google Scholar]
- M.d.M. González Nogueras, M.P. Gualdani and J.d. Solà-Morales Rubió, Instability and bifurcation in a trend depending price formation model. Acta Appl. Math. 144 (2016) 121–136. [CrossRef] [MathSciNet] [Google Scholar]
- P. Grover, K. Bakshi and E.A. Theodorou, A mean-field game model for homogeneous flocking. Chaos 28 (2018) 061103. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- L. Stella, D. Bauso and P. Colaneri, Mean-field game for collective decision-making in honeybees via switched systems. IEEE Trans. Automatic Control 67 (2021) 3863–3878. [Google Scholar]
- Y. Xu, Z. Yang, W. Gu, et al., Robust real-time distributed optimal control based energy management in a smart grid. IEEE Trans. Smart Grid 8 (2015) 1568–1579. [Google Scholar]
- A. Seguret, C. Wan and C. Alasseur, A mean field control approach for smart charging with aggregate power demand constraints, in 2021 IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe). IEEE (2021) 01–05. [Google Scholar]
- M. Tan and Q. Le, EfficientNet: rethinking model scaling for convolutional neural networks. Chaudhuri K, Salakhutdinov R. Proceedings of Machine Learning Research: Vol. 97. Proceedings of the 36th International Conference on Machine Learning. PMLR (2019) 6105–6114. https://proceedings.mlr.press/v97/tan19a.html. [Google Scholar]
- A. Cavagna, A. Cimarelli, I. Giardina, et al., Scale-free correlations in starling flocks. Proc. Natl. Acad. Sci. 107 (2010) 11865–11870. [CrossRef] [PubMed] [Google Scholar]
- T. Mora and W. Bialek, Are biological systems poised at criticality?. J. Stat. Phys. 144 (2011) 268–302. [CrossRef] [MathSciNet] [Google Scholar]
- J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. U.S.A. 79 (1982) 2554–2558. [CrossRef] [PubMed] [Google Scholar]
- D.R. Chialvo, Emergent complex neural dynamics. Nat. Phys. 6 (2010) 744–750. [CrossRef] [Google Scholar]
- F. Vanni, M. Lukovioć and P. Grigolini, Criticality and transmission of information in a swarm of cooperative units. Phys. Rev. Lett. 107 (2011) 078103. [CrossRef] [PubMed] [Google Scholar]
- R. Carmona, Q. Cormier and H.M. Soner, Synchronization in a kuramoto mean field game. Commun. Partial Differ. Equa. (2023) 1–31. [Google Scholar]
- A. De Masi, E. Orlandi, E. Presutti, et al., Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics. Nonlinearity 7 (1994) 633. [CrossRef] [MathSciNet] [Google Scholar]
- A.D. Masi, E. Orlandi, E. Presutti, et al., Glauber evolution with Kac potentials. II. Fluctuations. Nonlinearity 9 (1996) 27–51. [CrossRef] [MathSciNet] [Google Scholar]
- A. De Masi, E. Orlandi, E. Presutti, et al., Glauber evolution with Kac potentials. III. Spinodal decomposition. Nonlinearity 9 (1996) 53. [CrossRef] [MathSciNet] [Google Scholar]
- U. Horst, Dynamic systems of social interactions. J. Econ. Behav. Organ. 73 (2010) 158–170. [CrossRef] [Google Scholar]
- U. Horst and J.A. Scheinkman, Equilibria in systems of social interactions. J. Econ. Theory 130 (2006) 44–77. [CrossRef] [Google Scholar]
- F. Collet, M. Formentin and D. Tovazzi, Rhythmic behavior in a two-population mean-field Ising model. Phys. Rev. E 94 (2016) 042139. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Leonidov, A. Savvateev and A.G. Semenov, Ising game on graphs. (2021). [Google Scholar]
- A. Seguret, Mean field approximation of an optimal control problem for the continuity equation arising in smart charging. Appl. Math. Optim. 88 (2023) 1–44. [CrossRef] [Google Scholar]
- R. Carmona, F. Delarue, et al., Probabilistic Theory of Mean Field Games with Applications I–II. Springer (2018). [Google Scholar]
- D.A. Gomes, J. Mohr and R.R. Souza, Continuous time finite state mean field games. Appl. Math. Optim. 68 (2013) 99–143. [Google Scholar]
- V.N. Kolokoltsov and A. Bensoussan, Mean-field-game model for botnet defense in cyber-security. Appl. Math. Optim. 74 (2016) 669–692. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bayraktar and A. Cohen, Analysis of a finite state many player game using its master equation. SIAM J. Control Optim. 56 (2018) 3538–3568. [CrossRef] [MathSciNet] [Google Scholar]
- A. Cecchin and G. Pelino, Convergence, fluctuations and large deviations for finite state mean field games via the master equation. Stochast. Processes Appl. 129 (2019) 4510–4555. [CrossRef] [Google Scholar]
- M. Cirant and G. Verzini, Bifurcation and segregation in quadratic two-populations mean field games systems. ESAIM: Control Optim. Calc. Var. 23 (2017) 1145–1177. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- M. Bardi and M. Fischer, On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM: Control Optim. Calc. Var. 25 (2019) 44. [CrossRef] [EDP Sciences] [Google Scholar]
- E. Bayraktar and X. Zhang, On non-uniqueness in mean field games. Proc. Am. Math. Soc. 148 (2020) 4091–4106. [CrossRef] [Google Scholar]
- P. Cardaliaguet, F. Delarue, J.M. Lasry, et al., The Master Equation and the Convergence Problem in Mean Field Games (ams-201). Princeton University Press (2019). [Google Scholar]
- D. Lacker, On the convergence of closed-loop Nash equilibria to the mean field game limit. Ann. Appl. Probab. 30 (2020) 1693–1761. [CrossRef] [MathSciNet] [Google Scholar]
- P. Cardaliaguet and M. Masoero, Weak KAM theory for potential MFG. J. Difer. Equ. 268 (2020) 3255–3298. [CrossRef] [Google Scholar]
- M. Masoero, On the long time convergence of potential MFG. Nonlinear Differ. Equ. Appl. 26 (2019) 1–45. [CrossRef] [Google Scholar]
- A. Cesaroni and M. Cirant, Stationary equilibria and their stability in a kuramoto mfg with strong interaction. Commun. Partial Difer. Equ. 49 (2024) 121–147. [CrossRef] [Google Scholar]
- T. Bodineau, The Wulff construction in three and more dimensions. Commun. Math. Phys. 207 (1999) 197–229. [CrossRef] [Google Scholar]
- G. Alberti, G. Bellettini, M. Cassandro, et al., Surface tension in Ising systems with Kac potentials. J. Stat. Phys. 82 (1996) 743–796. [CrossRef] [Google Scholar]
- L.C. Evans, H.M. Soner and P.E. Souganidis, Phase transitions and generalized motion by mean curvature. Commun. Pure Appl. Math. 45 (1992) 1097–1123. [Google Scholar]
- M.A. Katsoulakis and P.E. Souganidis, Generalized motion by mean curvature as a macroscopic limit of stochastic Ising models with long range interactions and Glauber dynamics. Commun. Math. Phys. 169 (1995) 61–97. [CrossRef] [Google Scholar]
- L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123–142. [CrossRef] [MathSciNet] [Google Scholar]
- G. Bouchitté, Singular perturbations of variational problems arising from a two-phase transition model. Appl. Math. Optim. 21 (1990) 289–314. [CrossRef] [MathSciNet] [Google Scholar]
- G. Alberti and G. Bellettini, A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies. Eur. J. Appl. Math. 9 (1998) 261–284. [CrossRef] [Google Scholar]
- S. Conti, I. Fonseca and G. Leoni, A Γ-convergence result for the two-gradient theory of phase transitions. Commun. Pure Appl. Math. 55 (2002) 857–936. [CrossRef] [Google Scholar]
- E. Sandier and S. Serfaty, Gamma-convergence of gradient flows with applications to Ginzburg–Landau. Commun. Pure Appl. Math. 57 (2004) 1627–1672. [CrossRef] [Google Scholar]
- A. Bressan, M.T. Chiri and N. Salehi, Optimal control of moving sets. Submitted, 2021. [Google Scholar]
- A. Bressan, M.T. Chiri and N. Salehi, On the optimal control of propagation fronts. (2021). [Google Scholar]
- J. Simons, Minimal varieties in Riemannian manifolds. Ann. Math. (1968) 62–105. [CrossRef] [MathSciNet] [Google Scholar]
- F. Morgan, The cone over the Clifford torus in ℝ4 is Φ-minimizing. Math. Ann. 289 (1991) 341–354. [CrossRef] [MathSciNet] [Google Scholar]
- G. Alberti and G. Bellettini, A nonlocal anisotropic model for phase transitions. Math. Ann. 310 (1998) 527–560. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Tonegawa and N. Wickramasekera, Stable phase interfaces in the van der Waals–Cahn–Hilliard theory. J. Angew. Math. 2012 (2012) 191–210. [Google Scholar]
- O. Chodosh and C. Mantoulidis, Minimal surfaces and the Allen–Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates. Ann. Math. 191 (2020) 213–328. [CrossRef] [MathSciNet] [Google Scholar]
- W. Gangbo, A.R. Mészáros, C. Mou, et al., Mean field games master equations with nonseparable hamiltonians and displacement monotonicity. Ann. Probab. 50 (2022) 2178–2217. [CrossRef] [MathSciNet] [Google Scholar]
- F. Delarue, D. Lacker and K. Ramanan, et al., From the master equation to mean field game limit theory: a central limit theorem. Electron. J. Probab. (2019) 24. [Google Scholar]
- L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Routledge (2018). [CrossRef] [Google Scholar]
- I. Fonseca and S. Müller, Relaxation of quasiconvex functional in BV(Ω, ℝp) for integrands f (x, u, ∇u). Arch. Rational Mech. Anal. 123 (1993) 1–49. [CrossRef] [MathSciNet] [Google Scholar]
- L.C. Evans and R.F. Gariepy, Blowup, compactness and partial regularity in the calculus of variations. Indiana Univ. Math. J. 36 (1987) 361–371. [CrossRef] [MathSciNet] [Google Scholar]
- D. Spector, Simple proofs of some results of Reshetnyak. Proc. Am. Math. Soc. (2011) 1681–1690. [CrossRef] [Google Scholar]
- E. Giusti and G.H. Williams, Minimal Surfaces and Functions of Bounded Variation, Vol. 80. Springer (1984). [CrossRef] [Google Scholar]
- A. Farah, Proving the regularity of the reduced boundary of perimeter minimizing sets with the De Giorgi lemma. (2020). [Google Scholar]
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