1932

Abstract

We review classic results and recent progress on equilibrium analysis, dynamics, and optimal interventions in network games with both continuous and discrete strategy sets. We study strategic interactions in deterministic networks as well as networks generated from a stochastic network formation model. For the former case, we review a unifying framework for analysis based on the theory of variational inequalities. For the latter case, we highlight how knowledge of the stochastic network formation model can be used by a central planner to design interventions for large networks in a computationally efficient manner when exact network data are not available.

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2021-05-03
2024-10-12
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Literature Cited

  1. 1. 
    Jackson MO. 2010. Social and Economic Networks Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  2. 2. 
    Easley D, Kleinberg J. 2010. Networks, Crowds, and Markets Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  3. 3. 
    Jackson MO, Zenou Y 2014. Games on networks. Handbook of Game Theory, Vol. 4 HP Young, S Zamir 95–163 Amsterdam: Elsevier
    [Google Scholar]
  4. 4. 
    Bramoullé Y, Kranton R 2016. Games played on networks. The Oxford Handbook of the Economics of Networks Y Bramoullé, A Galeotti, BW Rogers 83–112 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  5. 5. 
    Bullo F. 2019. Lectures on Network Systems Seattle, WA: Kindle Direct Publ.
    [Google Scholar]
  6. 6. 
    Bramoullé Y, Kranton R. 2007. Public goods in networks. J. Econ. Theory 135:478–94
    [Google Scholar]
  7. 7. 
    Dubey P, Haimanko O, Zapechelnyuk A. 2006. Strategic complements and substitutes, and potential games. Games Econ. Behav. 54:77–94
    [Google Scholar]
  8. 8. 
    Menache I, Ozdaglar A. 2011. Network games: theory, models, and dynamics. Synth. Lect. Commun. Netw. 4:75
    [Google Scholar]
  9. 9. 
    Marden JR, Shamma JS. 2018. Game theory and control. Annu. Rev. Control Robot. Auton. Syst. 1:105–34
    [Google Scholar]
  10. 10. 
    Vives X. 2005. Complementarities and games: new developments. J. Econ. Lit. 43:437–79
    [Google Scholar]
  11. 11. 
    Milgrom P, Roberts J. 1994. Comparing equilibria. Am. Econ. Rev. 84:441–59
    [Google Scholar]
  12. 12. 
    Milgrom P, Shannon C. 1994. Monotone comparative statics. Econometrica 62:157–80
    [Google Scholar]
  13. 13. 
    Fudenberg D, Tirole J. 1991. Game Theory Cambridge, MA: MIT Press
    [Google Scholar]
  14. 14. 
    Topkis DM. 2011. Supermodularity and Complementarity Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  15. 15. 
    Monderer D, Shapley LS. 1996. Potential games. Games Econ. Behav. 14:124–43
    [Google Scholar]
  16. 16. 
    Ballester C, Calvó-Armengol A, Zenou Y. 2006. Who's who in networks. Wanted: the key player. Econometrica 74:1403–17
    [Google Scholar]
  17. 17. 
    Bonacich P. 1987. Power and centrality: a family of measures. Am. J. Sociol. 92:1170–82
    [Google Scholar]
  18. 18. 
    Bramoullé Y, Kranton R, D'Amours M. 2014. Strategic interaction and networks. Am. Econ. Rev. 104:898–930
    [Google Scholar]
  19. 19. 
    Belhaj M, Deroïan F. 2014. Competing activities in social networks. B.E. J. Econ. Anal. Policy 14:1431–66
    [Google Scholar]
  20. 20. 
    Acemoglu D, Ozdaglar A, Tahbaz-Salehi A. 2015. Networks, shocks, and systemic risk. The Oxford Handbook of the Economics of Networks Y Bramoullé, A Galeotti, BW Rogers 569–607 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  21. 21. 
    Allouch N. 2015. On the private provision of public goods on networks. J. Econ. Theory 157:527–52
    [Google Scholar]
  22. 22. 
    Chen YJ, Zenou Y, Zhou J. 2018. Multiple activities in networks. Am. Econ. J. Microecon. 10:34–85
    [Google Scholar]
  23. 23. 
    Ui T. 2016. Bayesian Nash equilibrium and variational inequalities. J. Math. Econ. 63:139–46
    [Google Scholar]
  24. 24. 
    Melo E. 2017. A variational approach to network games. Work. Pap. 005.2018, Fond. Eni Enrico Mattei, Milan, It .
    [Google Scholar]
  25. 25. 
    Naghizadeh P, Liu M. 2017. On the uniqueness and stability of equilibria of network games. 2017 55th Annual Allerton Conference on Communication, Control, and Computing280–86 Piscataway, NJ: IEEE
    [Google Scholar]
  26. 26. 
    Parise F, Ozdaglar A. 2019. A variational inequality framework for network games: existence, uniqueness, convergence and sensitivity analysis. Games Econ. Behav. 114:47–82
    [Google Scholar]
  27. 27. 
    Scutari G, Palomar DP, Facchinei F, Pang JS. 2010. Convex optimization, game theory, and variational inequality theory. IEEE Signal Process. Mag. 27:335–49
    [Google Scholar]
  28. 28. 
    Facchinei F, Pang JS. 2003. Finite-Dimensional Variational Inequalities and Complementarity Problems New York: Springer
    [Google Scholar]
  29. 29. 
    Scutari G, Facchinei F, Pang JS, Palomar DP. 2014. Real and complex monotone communication games. IEEE Trans. Inf. Theory 60:4197–231
    [Google Scholar]
  30. 30. 
    Fiedler M, Ptak V. 1962. On matrices with non-positive off-diagonal elements and positive principal minors. Czech. Math. J. 12:382–400
    [Google Scholar]
  31. 31. 
    Bertsekas DP, Tsitsiklis JN. 1997. Parallel and Distributed Computation: Numerical Methods Nashua, NH: Athena Sci.
    [Google Scholar]
  32. 32. 
    Gadjov D, Pavel L 2018. A passivity-based approach to Nash equilibrium seeking over networks. IEEE Trans. Autom. Control 64:1077–92
    [Google Scholar]
  33. 33. 
    Ghaderi J, Srikant R. 2014. Opinion dynamics in social networks with stubborn agents: equilibrium and convergence rate. Automatica 50:3209–15
    [Google Scholar]
  34. 34. 
    DeGroot MH. 1974. Reaching a consensus. J. Am. Stat. Assoc. 69:118–21
    [Google Scholar]
  35. 35. 
    Sandholm WH. 2010. Population Games and Evolutionary Dynamics Cambridge, MA: MIT Press
    [Google Scholar]
  36. 36. 
    Galeotti A, Golub B, Goyal S. 2017. Targeting interventions in networks. arXiv:1710.06026 [cs.GT]
  37. 37. 
    Boyd S, Vandenberghe L. 2004. Convex Optimization Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  38. 38. 
    Candogan O, Bimpikis K, Ozdaglar A. 2012. Optimal pricing in networks with externalities. Oper. Res. 60:883–905
    [Google Scholar]
  39. 39. 
    Morris S. 2000. Contagion. Rev. Econ. Stud. 67:57–78
    [Google Scholar]
  40. 40. 
    Jackson MO, Storms E. 2019. Behavioral communities and the atomic structure of networks Work. Pap. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3049748
    [Google Scholar]
  41. 41. 
    Granovetter M. 1978. Threshold models of collective behavior. Am. J. Sociol. 83:1420–43
    [Google Scholar]
  42. 42. 
    Liggett TM. 2012. Interacting Particle Systems Berlin: Springer
    [Google Scholar]
  43. 43. 
    Durrett R. 1988. Lecture Notes on Particle Systems and Percolation Pacific Grove, CA: Wadsworth
    [Google Scholar]
  44. 44. 
    Goldenberg J, Libai B, Muller E. 2001. Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark. Lett. 12:211–23
    [Google Scholar]
  45. 45. 
    Goldenberg A, Zheng AX, Fienberg SE, Airoldi EM. 2010. A survey of statistical network models. Found. Trends Mach. Learn. 2:129–233
    [Google Scholar]
  46. 46. 
    Centola D, Macy M 2007. Complex contagions and the weakness of long ties. Am. J. Sociol. 113:702–34
    [Google Scholar]
  47. 47. 
    Centola D. 2018. How Behavior Spreads: The Science of Complex Contagions Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  48. 48. 
    Young HP. 2009. Innovation diffusion in heterogeneous populations: contagion, social influence, and social learning. Am. Econ. Rev. 99:1899–924
    [Google Scholar]
  49. 49. 
    Acemoglu D, Ozdaglar A, Yildiz E. 2011. Diffusion of innovations in social networks. 2011 50th IEEE Conference on Decision and Control and European Control Conference2329–34 Piscataway, NJ: IEEE
    [Google Scholar]
  50. 50. 
    Galeotti A, Goyal S. 2009. Influencing the influencers: a theory of strategic diffusion. RAND J. Econ. 40:509–32
    [Google Scholar]
  51. 51. 
    Bloch F, Demange G, Kranton R. 2018. Rumors and social networks. Int. Econ. Rev. 59:421–48
    [Google Scholar]
  52. 52. 
    Sadler E. 2020. Diffusion games. Am. Econ. Rev. 110:225–70
    [Google Scholar]
  53. 53. 
    Goyal S, Heidari H, Kearns M. 2019. Competitive contagion in networks. Games Econ. Behav. 113:58–79
    [Google Scholar]
  54. 54. 
    Fazeli A, Jadbabaie A. 2012. Game theoretic analysis of a strategic model of competitive contagion and product adoption in social networks. 2012 IEEE 51st IEEE Conference on Decision and Control74–79 Piscataway, NJ: IEEE
    [Google Scholar]
  55. 55. 
    Draief M, Heidari H, Kearns M. 2014. New models for competitive contagion. Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence637–44 Palo Alto, CA: AAAI Press
    [Google Scholar]
  56. 56. 
    Tzoumas V, Amanatidis C, Markakis E. 2012. A game-theoretic analysis of a competitive diffusion process over social networks. Internet and Network Economics: 8th International Workshop WINE 2012, ed. PW Goldberg 1–14 Berlin: Springer
    [Google Scholar]
  57. 57. 
    Fazeli A, Ajorlou A, Jadbabaie A. 2016. Competitive diffusion in social networks: quality or seeding?. IEEE Trans. Control Netw. Syst. 4:665–75
    [Google Scholar]
  58. 58. 
    Mei W, Bullo F. 2017. Competitive propagation: models, asymptotic behavior and quality-seeding games. IEEE Trans. Netw. Sci. Eng. 4:83–99
    [Google Scholar]
  59. 59. 
    Nowzari C, Preciado VM, Pappas GJ. 2016. Analysis and control of epidemics: a survey of spreading processes on complex networks. IEEE Control Syst. Mag. 36:126–46
    [Google Scholar]
  60. 60. 
    Adam EM, Dahleh MA, Ozdaglar A. 2012. On the behavior of threshold models over finite networks. 2012 IEEE 51st IEEE Conference on Decision and Control2672–77 Piscataway, NJ: IEEE
    [Google Scholar]
  61. 61. 
    Young HP 2006. The diffusion of innovations in social networks. The Economy as an Evolving Complex System, III: Current Perspectives and Future Directions LE Blume, SN Durlauf 267–82 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  62. 62. 
    Montanari A, Saberi A 2010. The spread of innovations in social networks. PNAS 107:20196–201
    [Google Scholar]
  63. 63. 
    Kempe D, Kleinberg J, Tardos É. 2003. Maximizing the spread of influence through a social network. Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining137–46 New York: ACM
    [Google Scholar]
  64. 64. 
    Lim Y, Ozdaglar A, Teytelboym A. 2016. A simple model of cascades in networks Work. Pap. http://t8el.com/wp-content/uploads/2015/08/SimpleCascades.pdf
    [Google Scholar]
  65. 65. 
    Liu-Thompkins Y. 2012. Seeding viral content: the role of message and network factors. J. Advert. Res. 52:465–78
    [Google Scholar]
  66. 66. 
    Breza E, Chandrasekhar AG, McCormick TH, Pan M. 2018. Using aggregated relational data to feasibly identify network structure without network data. arXiv:1703.04157 [stat.ME]
  67. 67. 
    Parise F, Ozdaglar A. 2019. Graphon games. Proceedings of the 2019 ACM Conference on Economics and Computation457–58 New York: ACM
    [Google Scholar]
  68. 68. 
    Mele A, Hao L, Cape J, Priebe CE. 2019. Spectral inference for large stochastic blockmodels with nodal covariates. arXiv:1908.06438 [stat.ME]
  69. 69. 
    Bollobás B, Béla B. 2001. Random Graphs Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  70. 70. 
    Pin P, Rogers B 2015. Stochastic network formation and homophily. The Oxford Handbook of the Economics of Networks Y Bramoullé, A Galeotti, BW Rogers 138–66 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  71. 71. 
    Newman MEJ, Strogatz SH, Watts DJ. 2001. Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64:026118
    [Google Scholar]
  72. 72. 
    Newman MEJ. 2010. Networks: An Introduction Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  73. 73. 
    Erdős P, Rényi A. 1959. On random graphs. Publ. Math. Debrecen 6:290–97
    [Google Scholar]
  74. 74. 
    McPherson M, Smith-Lovin L, Cook JM. 2001. Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27:415–44
    [Google Scholar]
  75. 75. 
    Currarini S, Jackson MO, Pin P. 2009. An economic model of friendship: homophily, minorities, and segregation. Econometrica 77:1003–45
    [Google Scholar]
  76. 76. 
    Golub B, Jackson MO 2012. How homophily affects the speed of learning and best-response dynamics. Q. J. Econ. 127:1287–338
    [Google Scholar]
  77. 77. 
    Bender EA, Canfield ER. 1978. The asymptotic number of labeled graphs with given degree sequences. J. Comb. Theory A 24:296–307
    [Google Scholar]
  78. 78. 
    Janson S, Luczak MJ. 2009. A new approach to the giant component problem. Random Struct. Algorithms 34:197–216
    [Google Scholar]
  79. 79. 
    Bordenave C. 2012. Lecture notes on random graphs and probabilistic combinatorial optimization Work. Pap. https://www.math.univ-toulouse.fr/∼bordenave/coursRG.pdf
    [Google Scholar]
  80. 80. 
    Lovász L, Szegedy B. 2006. Limits of dense graph sequences. J. Comb. Theory B 96:933–57
    [Google Scholar]
  81. 81. 
    Lovász L. 2012. Large Networks and Graph Limits Providence, RI: Am. Math. Soc.
    [Google Scholar]
  82. 82. 
    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. 219:1801–51
    [Google Scholar]
  83. 83. 
    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. Am. Math. Soc. 372:3019–62
    [Google Scholar]
  84. 84. 
    Borgs C, Chayes JT, Lovász L, Sós VT, Vesztergombi K. 2011. Limits of randomly grown graph sequences. Eur. J. Comb. 32:985–99
    [Google Scholar]
  85. 85. 
    Dasaratha K. 2017. Distributions of centrality on networks. arXiv:1709.10402 [cs.SI]
  86. 86. 
    Avella-Medina M, Parise F, Schaub M, Segarra S. 2018. Centrality measures for graphons: accounting for uncertainty in networks. arXiv:1707.09350 [cs.SI]
  87. 87. 
    Akbarpour M, Malladi S, Saberi A. 2018. Just a few seeds more: value of network information for diffusion Work. Pap. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3062830
    [Google Scholar]
  88. 88. 
    Moharrami M, Subramanian V, Liu M, Lelarge M. 2016. Impact of community structure on cascades. Proceedings of the 2016 ACM Conference on Economics and Computation635–36 New York: ACM
    [Google Scholar]
  89. 89. 
    Erol S, Parise F, Teytelboym A. 2020. Contagion in graphons. Proceedings of the 2020 ACM Conference on Economics and Computation469 New York: ACM
    [Google Scholar]
  90. 90. 
    Watts DJ. 2002. A simple model of global cascades on random networks. PNAS 99:5766–71
    [Google Scholar]
  91. 91. 
    Amini H. 2010. Bootstrap percolation and diffusion in random graphs with given vertex degrees. Electron. J. Comb. 17:R25
    [Google Scholar]
  92. 92. 
    Lelarge M. 2012. Diffusion and cascading behavior in random networks. Games Econ. Behav. 75:752–75
    [Google Scholar]
  93. 93. 
    Baxter GJ, Dorogovtsev SN, Goltsev AV, Mendes JF. 2010. Bootstrap percolation on complex networks. Phys. Rev. E 82:011103
    [Google Scholar]
  94. 94. 
    Rossi WS, Como G, Fagnani F. 2017. Threshold models of cascades in large-scale networks. IEEE Trans. Netw. Sci. Eng. 6:158–72
    [Google Scholar]
  95. 95. 
    Amini H, Cont R, Minca A. 2016. Resilience to contagion in financial networks. Math. Finance 26:329–65
    [Google Scholar]
  96. 96. 
    Galeotti A, Goyal S, Jackson MO, Vega-Redondo F, Yariv L 2010. Network games. Rev. Econ. Stud. 77:218–44
    [Google Scholar]
  97. 97. 
    Kalai E. 2004. Large robust games. Econometrica 72:1631–65
    [Google Scholar]
  98. 98. 
    Eksin C, Molavi P, Ribeiro A, Jadbabaie A. 2013. Learning in network games with incomplete information: asymptotic analysis and tractable implementation of rational behavior. IEEE Signal Process. Mag. 30:330–42
    [Google Scholar]
  99. 99. 
    Bramoullé Y, Djebbari H, Fortin B. 2009. Identification of peer effects through social networks. J. Econom. 150:41–55
    [Google Scholar]
  100. 100. 
    Chandrasekhar A, Lewis R. 2016. Econometrics of sampled networks Work. Pap. http://stanford.edu/∼arungc/CL.pdf
    [Google Scholar]
  101. 101. 
    De Paula A, Rasul I, Souza P. 2018. Recovering social networks from panel data: identification, simulations and an application Work. Pap. 0001 Latin Am. Caribb. Econ. Assoc New York: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3322049
    [Google Scholar]
  102. 102. 
    Boucher V, Houndetoungan A. 2019. Estimating peer effects using partial network data Work. Pap., Cent. Rech. Risques Enjeux Écon. Politiques Publiques, Univ. Laval Quebec, Can: https://www.crrep.ca/sites/crrep.ca/files/fichier_publications/2020-07.pdf
    [Google Scholar]
  103. 103. 
    Lewbel A, Qu X, Tang X. 2019. Social networks with misclassified or unobserved links Work. Pap. 1004 Dep. Econ., Boston Coll Boston: https://www.tang-xun.com/uploads/4/8/0/5/48051869/miscont_june2019_v2.pdf
    [Google Scholar]
  104. 104. 
    Stein S, Eshghi S, Maghsudi S, Tassiulas L, Bellamy RK, Jennings NR 2017. Heuristic algorithms for influence maximization in partially observable social networks. Proceedings of the 3rd International Workshop on Social Influence Analysis MG Armentano, J Tang, V Yannibelli 20–32 N.p: MG Armentano, J Tang, and V Yannibelli
    [Google Scholar]
  105. 105. 
    Wilder B, Immorlica N, Rice E, Tambe M 2018. Maximizing influence in an unknown social network. Thirty-Second AAAI Conference on Artificial Intelligence4743–50 Palo Alto, CA: AAAI Press
    [Google Scholar]
  106. 106. 
    Eckles D, Esfandiari H, Mossel E, Rahimian MA. 2019. Seeding with costly network information Work. Pap. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3386417
    [Google Scholar]
  107. 107. 
    Chin A, Eckles D, Ugander J. 2018. Evaluating stochastic seeding strategies in networks. arXiv:1809.09561 [stat.ME]
  108. 108. 
    Banerjee A, Chandrasekhar AG, Duflo E, Jackson MO 2019. Using gossips to spread information: theory and evidence from two randomized controlled trials. Rev. Econ. Stud. 86:2453–90
    [Google Scholar]
  109. 109. 
    Quijano N, Ocampo-Martinez C, Barreiro-Gomez J, Obando G, Pantoja A, Mojica-Nava E. 2017. The role of population games and evolutionary dynamics in distributed control systems: the advantages of evolutionary game theory. IEEE Control Syst. Mag. 37:170–97
    [Google Scholar]
  110. 110. 
    Lasry JM, Lions PL. 2007. Mean field games. Jpn. J. Math. 2:229–60
    [Google Scholar]
  111. 111. 
    Huang M, Caines PE, Malhamé RP. 2007. Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε-Nash equilibria. IEEE Trans. Autom. Control 52:1560–71
    [Google Scholar]
  112. 112. 
    Sandholm WH. 2001. Potential games with continuous player sets. J. Econ. Theory 97:81–108
    [Google Scholar]
  113. 113. 
    Hofbauer J, Sandholm WH. 2009. Stable games and their dynamics. J. Econ. Theory 144:1665–93
    [Google Scholar]
  114. 114. 
    Fox MJ, Shamma JS 2013. Population games, stable games, and passivity. Games 4:561–83
    [Google Scholar]
  115. 115. 
    Gao B, Pavel L 2021. On passivity, reinforcement learning, and higher order learning in multiagent finite games. IEEE Trans. Autom. Control 66:12136
    [Google Scholar]
  116. 116. 
    Park S, Martins NC, Shamma JS. 2019. Payoff dynamics model and evolutionary dynamics model: feedback and convergence to equilibria. arXiv:1903.02018 [math.OC]
  117. 117. 
    Caines PE, Huang M. 2018. Graphon Mean Field Games and the GMFG equations. 2018 IEEE Conference on Decision and Control4129–34 Piscataway, NJ: IEEE
    [Google Scholar]
  118. 118. 
    Caines PE, Huang M. 2019. Graphon Mean Field Games and the GMFG equations: ε-Nash equilibria. 2019 IEEE 58th Conference on Decision and Control286–92 Piscataway, NJ: IEEE
    [Google Scholar]
  119. 119. 
    Carmona R, Cooney D, Graves C, Lauriere M. 2019. Stochastic graphon games: I. The static case. arXiv:1911.10664 [math.OC]
  120. 120. 
    Kukushkin NS. 2004. Best response dynamics in finite games with additive aggregation. Games Econ. Behav. 48:94110
    [Google Scholar]
  121. 121. 
    Jensen MK. 2010. Aggregative games and best-reply potentials. Econ. Theory 43:45–66
    [Google Scholar]
  122. 122. 
    Cornes R, Hartley R. 2012. Fully aggregative games. Econ. Lett. 116:631–33
    [Google Scholar]
  123. 123. 
    Jensen MK. 2005. Existence, comparative statics and stability in games with strategic substitutes Work. Pap., Dep. Econ., Birmingham Univ Birmingham, UK: http://www.gtcenter.org/Archive/Conf06/Downloads/Conf/Jensen60.pdf
    [Google Scholar]
  124. 124. 
    Acemoglu D, Jensen MK. 2013. Aggregate comparative statics. Games Econ. Behav. 81:27–49
    [Google Scholar]
  125. 125. 
    Jensen MK. 2018. Aggregative games. Handbook of Game Theory and Industrial Organization, Vol. 1: Theory Cheltenham, UK: Edward Elgar
    [Google Scholar]
  126. 126. 
    Ma Z, Callaway DS, Hiskens IA. 2013. Decentralized charging control of large populations of plug-in electric vehicles. IEEE Trans. Control Syst. Technol. 21:67–78
    [Google Scholar]
  127. 127. 
    Chen H, Li Y, Louie RHY, Vucetic B. 2014. Autonomous demand side management based on energy consumption scheduling and instantaneous load billing: an aggregative game approach. IEEE Trans. Smart Grid 5:1744–54
    [Google Scholar]
  128. 128. 
    Koshal J, Nedić A, Shanbhag UV. 2016. Distributed algorithms for aggregative games on graphs. Oper. Res. 64:680–704
    [Google Scholar]
  129. 129. 
    Grammatico S, Parise F, Colombino M, Lygeros J. 2016. Decentralized convergence to Nash equilibria in constrained deterministic mean field control. IEEE Trans. Autom. Control 61:3315–29
    [Google Scholar]
  130. 130. 
    Paccagnan D, Kamgarpour M, Lygeros J. 2016. On aggregative and mean field games with applications to electricity markets. 2016 European Control Conference196–201 Piscataway, NJ: IEEE
    [Google Scholar]
  131. 131. 
    Liang S, Yi P, Hong Y 2017. Distributed Nash equilibrium seeking for aggregative games with coupled constraints. Automatica 85:179–85
    [Google Scholar]
  132. 132. 
    Grammatico S. 2017. Dynamic control of agents playing aggregative games with coupling constraints. IEEE Trans. Autom. Control 62:4537–48
    [Google Scholar]
  133. 133. 
    Grammatico S. 2017. Proximal dynamics in multiagent network games. IEEE Trans. Control Netw. Syst. 5:1707–16
    [Google Scholar]
  134. 134. 
    Paccagnan D, Gentile B, Parise F, Kamgarpour M, Lygeros J. 2018. Nash and Wardrop equilibria in aggregative games with coupling constraints. IEEE Trans. Autom. Control 64:1373–88
    [Google Scholar]
  135. 135. 
    De Persis C, Grammatico S. 2019. Continuous-time integral dynamics for a class of aggregative games with coupling constraints. IEEE Trans. Autom. Control 65:2171–76
    [Google Scholar]
  136. 136. 
    Parise F, Gentile B, Lygeros J. 2019. A distributed algorithm for almost-Nash equilibria of average aggregative games with coupling constraints. IEEE Trans. Control Netw. Syst. 7:770–82
    [Google Scholar]
  137. 137. 
    Gadjov D, Pavel L 2019. Single-timescale distributed GNE seeking for aggregative games over networks via forward-backward operator splitting. arXiv:1908.00107 [math.OC]
  138. 138. 
    Belgioioso G, Nedich A, Grammatico S. 2020. Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks. IEEE Trans. Autom. Control In press. https://doi.org/10.1109/TAC.2020.3005922
    [Crossref] [Google Scholar]
  139. 139. 
    Parise F, Grammatico S, Gentile B, Lygeros J. 2020. Distributed convergence to Nash equilibria in network and average aggregative games. Automatica 117:108959
    [Google Scholar]
  140. 140. 
    Kearns M, Littman ML, Singh S. 2001. Graphical models for game theory. Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence253–60 San Francisco, CA: Morgan Kaufmann
    [Google Scholar]
  141. 141. 
    Kakade SM, Kearns M, Ortiz LE 2004. Graphical economics. Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004 J Shawe-Taylor, Y Singer 17–32 Berlin: Springer
    [Google Scholar]
  142. 142. 
    Bala V, Goyal S. 2000. A noncooperative model of network formation. Econometrica 68:1181–229
    [Google Scholar]
  143. 143. 
    Pagan N, Dörfler F. 2019. Game theoretical inference of human behavior in social networks. Nat. Commun. 10:5507
    [Google Scholar]
  144. 144. 
    Erol S. 2018. Network hazard and bailouts Work. Pap. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3034406
    [Google Scholar]
  145. 145. 
    Chasparis GC, Shamma JS. 2012. Distributed dynamic reinforcement of efficient outcomes in multiagent coordination and network formation. Dyn. Games Appl. 2:18–50
    [Google Scholar]
  146. 146. 
    Chasparis GC, Shamma JS. 2013. Network formation: neighborhood structures, establishment costs, and distributed learning. IEEE Trans. Cybern. 43:1950–62
    [Google Scholar]
  147. 147. 
    Acemoglu D, Malekian A, Ozdaglar A. 2016. Network security and contagion. J. Econ. Theory 166:536–85
    [Google Scholar]
  148. 148. 
    Blume L, Easley D, Kleinberg J, Kleinberg R, Tardos É. 2013. Network formation in the presence of contagious risk. ACM Trans. Econ. Comput. 1:6
    [Google Scholar]
  149. 149. 
    Acemoglu D, Makhdoumi A, Malekian A, Ozdaglar A. 2017. Privacy-constrained network formation. Games Econ. Behav. 105:255–75
    [Google Scholar]
  150. 150. 
    Eksin C, Shamma JS, Weitz JS. 2017. Disease dynamics in a stochastic network game: A little empathy goes a long way in averting outbreaks. Sci. Rep. 7:44122
    [Google Scholar]
  151. 151. 
    Ajorlou A, Jadbabaie A, Kakhbod A. 2018. Dynamic pricing in social networks: the word-of-mouth effect. Manag. Sci. 64:971–79
    [Google Scholar]
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