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Published in: Dynamic Games and Applications 4/2019

31-01-2019

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

Authors: Paolo Dai Pra, Elena Sartori, Marco Tolotti

Published in: Dynamic Games and Applications | Issue 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.

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Appendix
Available only for authorised users
Footnotes
1
For recent literature investigating the relationship between the network geometry and the diffusion of knowledge, innovation, consensus, see [20, 27, 34, 36].
 
Literature
1.
go back to reference Akerlof GA (1997) Social distance and social decisions. Econ J Econ Soc 65(5):1005–1027 MathSciNet Akerlof GA (1997) Social distance and social decisions. Econ J Econ Soc 65(5):1005–1027 MathSciNet
2.
go back to reference Bagagiolo F, Bauso D, Pesenti R (2016) Mean-field game modeling the bandwagon effect with activation costs. Dyn Games Appl 6(4):456–476 MathSciNetCrossRef Bagagiolo F, Bauso D, Pesenti R (2016) Mean-field game modeling the bandwagon effect with activation costs. Dyn Games Appl 6(4):456–476 MathSciNetCrossRef
3.
go back to reference Bardi M, Fischer M (2018) On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM Control Optim Calc Var Bardi M, Fischer M (2018) On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM Control Optim Calc Var
4.
go back to reference Bauso D, Pesenti R, Tolotti M (2016) Opinion dynamics and stubbornness via multi-population mean-field games. J Optim Theory Appl 170(1):266–293 MathSciNetCrossRef Bauso D, Pesenti R, Tolotti M (2016) Opinion dynamics and stubbornness via multi-population mean-field games. J Optim Theory Appl 170(1):266–293 MathSciNetCrossRef
6.
go back to reference 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 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
7.
go back to reference 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, 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
10.
go back to reference Challet D, Zhang Y-C (1997) Emergence of cooperation and organization in an evolutionary game. Phys A Stat Mech Appl 246(3–4):407–418 CrossRef Challet D, Zhang Y-C (1997) Emergence of cooperation and organization in an evolutionary game. Phys A Stat Mech Appl 246(3–4):407–418 CrossRef
11.
go back to reference Collet F, Dai Pra P, Formentin M (2015) Collective periodicity in mean-field models of cooperative behavior. NoDEA Nonlinear Differ Equ Appl 22(5):1461–1482 MathSciNetCrossRef Collet F, Dai Pra P, Formentin M (2015) Collective periodicity in mean-field models of cooperative behavior. NoDEA Nonlinear Differ Equ Appl 22(5):1461–1482 MathSciNetCrossRef
12.
13.
go back to reference Ditlevsen S, Löcherbach E (2017) Multi-class oscillating systems of interacting neurons. Stoch Process Appl 127(6):1840–1869 MathSciNetCrossRef Ditlevsen S, Löcherbach E (2017) Multi-class oscillating systems of interacting neurons. Stoch Process Appl 127(6):1840–1869 MathSciNetCrossRef
14.
go back to reference Epstein JM (2002) Modeling civil violence: an agent-based computational approach. Proc Natl Acad Sci 99(suppl 3):7243–7250 CrossRef Epstein JM (2002) Modeling civil violence: an agent-based computational approach. Proc Natl Acad Sci 99(suppl 3):7243–7250 CrossRef
16.
go back to reference 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 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
18.
go back to reference Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83(6):1420–1443 CrossRef Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83(6):1420–1443 CrossRef
19.
go back to reference 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 205–266 CrossRef 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 205–266 CrossRef
20.
21.
go back to reference 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 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.
go back to reference 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 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.
go back to reference 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):221–252 MathSciNetMATH 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):221–252 MathSciNetMATH
26.
go back to reference Lindner B, Garcıa-Ojalvo J, Neiman A, Schimansky-Geier L (2004) Effects of noise in excitable systems. Phys Rep 392(6):321–424 CrossRef Lindner B, Garcıa-Ojalvo J, Neiman A, Schimansky-Geier L (2004) Effects of noise in excitable systems. Phys Rep 392(6):321–424 CrossRef
27.
go back to reference Montanari A, Saberi A (2010) The spread of innovations in social networks. Proc Natl Acad Sci 107(47):20196–20201 CrossRef Montanari A, Saberi A (2010) The spread of innovations in social networks. Proc Natl Acad Sci 107(47):20196–20201 CrossRef
28.
go back to reference Ramazi P, Riehl J, Cao M (2016) Networks of conforming or nonconforming individuals tend to reach satisfactory decisions. Proc Natl Acad Sci 113(46):12985–12990 CrossRef Ramazi P, Riehl J, Cao M (2016) Networks of conforming or nonconforming individuals tend to reach satisfactory decisions. Proc Natl Acad Sci 113(46):12985–12990 CrossRef
29.
go back to reference Schelling T (1978) Micromotives and macrobehavior. Norton 372:373 Schelling T (1978) Micromotives and macrobehavior. Norton 372:373
30.
go back to reference Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1(2):143–186 CrossRef Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1(2):143–186 CrossRef
31.
go back to reference Schelling TC (1973) Hockey helmets, concealed weapons, and daylight saving: a study of binary choices with externalities. J Confl Resolut 17(3):381–428 CrossRef Schelling TC (1973) Hockey helmets, concealed weapons, and daylight saving: a study of binary choices with externalities. J Confl Resolut 17(3):381–428 CrossRef
32.
go back to reference 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 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
34.
go back to reference 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):1068–1073 CrossRef 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):1068–1073 CrossRef
35.
go back to reference 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):663–667 CrossRef 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):663–667 CrossRef
36.
go back to reference Young HP (2011) The dynamics of social innovation. Proc Natl Acad Sci 108(Supplement 4):21285–21291 CrossRef Young HP (2011) The dynamics of social innovation. Proc Natl Acad Sci 108(Supplement 4):21285–21291 CrossRef
Metadata
Title
Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions
Authors
Paolo Dai Pra
Elena Sartori
Marco Tolotti
Publication date
31-01-2019
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 4/2019
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-019-00299-y

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