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Dynamic Games and Applications

Erschienen in:

31.01.2019

Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions

verfasst von: Paolo Dai Pra, Elena Sartori, Marco Tolotti

Erschienen in: Dynamic Games and Applications | Ausgabe 4/2019

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Abstract

What is the emergent long-run equilibrium of a society, where many interacting agents bet on the optimal energy to put in place in order to climb on the Bandwagon? In this paper, we study the collective behavior of a large population of agents being either Left or Right: The core idea is that agents benefit from being with the winner party, but, on the other hand, they suffer a cost in changing their status quo. At the microscopic level, the model is formulated as a stochastic, symmetric dynamic game with N players. In the macroscopic limit as \(N \rightarrow +\,\infty \), the model can be rephrased as a mean field game, whose equilibria describe the “rational” collective behavior of the society. It is of particular interest to detect the emerging long time attractors, e.g., consensus or oscillating behavior. Significantly, we discover that bandwagoning can be persistent at the macrolevel: We provide evidence, also on the basis of numerical simulations, of endogenously generated periodicity.

Vorheriger Artikel Growth and Insecure Private Property of Capital

Nächster Artikel Generalized Cops and Robbers: A Multi-player Pursuit Game on Graphs

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For recent literature investigating the relationship between the network geometry and the diffusion of knowledge, innovation, consensus, see [20, 27, 34, 36].

Akerlof GA (1997) Social distance and social decisions. Econ J Econ Soc 65(5):1005–1027MathSciNet

Bagagiolo F, Bauso D, Pesenti R (2016) Mean-field game modeling the bandwagon effect with activation costs. Dyn Games Appl 6(4):456–476MathSciNetCrossRef

Bardi M, Fischer M (2018) On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM Control Optim Calc Var

Bauso D, Pesenti R, Tolotti M (2016) Opinion dynamics and stubbornness via multi-population mean-field games. J Optim Theory Appl 170(1):266–293MathSciNetCrossRef

Brock WA, Durlauf SN (2001) Discrete choice with social interactions. Rev Econ Stud 68(2):235–260MathSciNetCrossRef

Cardaliaguet P, Delarue F, Lasry J-M, Lions P-L (2015) The master equation and the convergence problem in mean field games. arXiv preprint arXiv:1509.02505

Cecchin A, Dai Pra P, Fischer M, Pelino G (2018) On the convergence problem in mean-field games: a two-state model without uniqueness. arXiv preprint arXiv:1810.05492

Cecchin A, Fischer M (2018) Probabilistic approach to finite state mean field games. Appl. Math. Optim. https://doi.org/10.1007/s00245-018-9488-7

Cecchin A, Pelino G (2018) Convergence, fluctuations and large deviations for finite state mean field games via the master equation. Stoch. Process. Their Appl. https://doi.org/10.1016/j.spa.2018.12.002.MathSciNetCrossRef

10.

Challet D, Zhang Y-C (1997) Emergence of cooperation and organization in an evolutionary game. Phys A Stat Mech Appl 246(3–4):407–418CrossRef

11.

Collet F, Dai Pra P, Formentin M (2015) Collective periodicity in mean-field models of cooperative behavior. NoDEA Nonlinear Differ Equ Appl 22(5):1461–1482MathSciNetCrossRef

12.

Dai Pra P, Fischer M, Regoli D (2013) A Curie–Weiss model with dissipation. J Stat Phys 152(1):37–53MathSciNetCrossRef

13.

Ditlevsen S, Löcherbach E (2017) Multi-class oscillating systems of interacting neurons. Stoch Process Appl 127(6):1840–1869MathSciNetCrossRef

14.

Epstein JM (2002) Modeling civil violence: an agent-based computational approach. Proc Natl Acad Sci 99(suppl 3):7243–7250CrossRef

15.

Föllmer H (1974) Random economies with many interacting agents. J Math Econ 1(1):51–62MathSciNetCrossRef

16.

Gao Z, Chen X, Liu J, Basar T (2016) Periodic behavior of a diffusion model over directed graphs. In: IEEE 55th conference on decision and control (CDC), 2016. IEEE

17.

Gomes DA et al (2014) Mean field games models—a brief survey. Dyn Games Appl 4(2):110–154MathSciNetCrossRef

18.

Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83(6):1420–1443CrossRef

19.

Guéant O, Lasry J-M, Lions P-L (2011) Mean, field games and applications. In: Paris–Princeton lectures on mathematical finance, 2010, vol. 2003 of lecture notes in mathematics. Springer, Berlin, pp 205–266CrossRef

20.

Horst U, Scheinkman JA (2006) Equilibria in systems of social interactions. J Econ Theory 130(1):44–77MathSciNetCrossRef

21.

Huang M, Caines PE, Malhamé RP (2003) Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions. In: Proceedings of 42nd IEEE conference on decision and control, 2003, vol 1. IEEE, pp 98–103

22.

Huang M, Malhamé RP, Caines PE (2005) Nash equilibria for large-population linear stochastic systems of weakly coupled agents. In: Analysis, control and optimization of complex dynamic systems, pp 215–252

23.

Huang M, Malhamé RP, Caines PE et al (2006) Large population stochastic dynamic games: closed-loop Mckean–Vlasov systems and the Nash certainty equivalence principle. Commun Inf Syst 6(3):221–252MathSciNetMATH

24.

Kalai E (2004) Large robust games. Econometrica 72(6):1631–1665MathSciNetCrossRef

25.

Lasry J-M, Lions P-L (2006) Jeux à champ moyen. i - le cas stationnaire. C R Math 343(9):619–625MathSciNetCrossRef

26.

Lindner B, Garcıa-Ojalvo J, Neiman A, Schimansky-Geier L (2004) Effects of noise in excitable systems. Phys Rep 392(6):321–424CrossRef

27.

Montanari A, Saberi A (2010) The spread of innovations in social networks. Proc Natl Acad Sci 107(47):20196–20201CrossRef

28.

Ramazi P, Riehl J, Cao M (2016) Networks of conforming or nonconforming individuals tend to reach satisfactory decisions. Proc Natl Acad Sci 113(46):12985–12990CrossRef

29.

Schelling T (1978) Micromotives and macrobehavior. Norton 372:373

30.

Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1(2):143–186CrossRef

31.

Schelling TC (1973) Hockey helmets, concealed weapons, and daylight saving: a study of binary choices with externalities. J Confl Resolut 17(3):381–428CrossRef

32.

Stella, L, Bagagiolo F, Bauso D, Como G (2013) Opinion dynamics and stubbornness through mean-field games. In: IEEE 52nd annual conference on decision and control (CDC), 2013. IEEE, pp 2519–2524

33.

Touboul J (2014) The hipster effect: when anticonformists all look the same. arXiv preprint arXiv:1410.8001

34.

Valori L, Picciolo F, Allansdottir A, Garlaschelli D (2012) Reconciling long-term cultural diversity and short-term collective social behavior. Proc Natl Acad Sci 109(4):1068–1073CrossRef

35.

Yang T, Meng Z, Dimarogonas DV, Johansson KH (2016) Periodic behaviors for discrete-time second-order multiagent systems with input saturation constraints. IEEE Trans Circuits Syst II Express Br 63(7):663–667CrossRef

36.

Young HP (2011) The dynamics of social innovation. Proc Natl Acad Sci 108(Supplement 4):21285–21291CrossRef

Titel: Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions
verfasst von: Paolo Dai Pra
Elena Sartori
Marco Tolotti
Publikationsdatum: 31.01.2019
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 4/2019
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-019-00299-y

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