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Dynamic Games and Applications

, Volume 1, Issue 1, pp 3–49 | Cite as

Opinion Dynamics and Learning in Social Networks

  • Daron Acemoglu
  • Asuman Ozdaglar
Article

Abstract

We provide an overview of recent research on belief and opinion dynamics in social networks. We discuss both Bayesian and non-Bayesian models of social learning and focus on the implications of the form of learning (e.g., Bayesian vs. non-Bayesian), the sources of information (e.g., observation vs. communication), and the structure of social networks in which individuals are situated on three key questions: (1) whether social learning will lead to consensus, i.e., to agreement among individuals starting with different views; (2) whether social learning will effectively aggregate dispersed information and thus weed out incorrect beliefs; (3) whether media sources, prominent agents, politicians and the state will be able to manipulate beliefs and spread misinformation in a society.

Keywords

Bayesian updating Consensus Disagreement Learning Misinformation Non-Bayesian models Rule of thumb behavior Social networks 

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References

  1. 1.
    Acemoglu D, Ozdaglar A, ParandehGheibi A (2010) Spread of (mis)information in social networks. Games Econ Behav, forthcoming Google Scholar
  2. 2.
    Acemoglu D, Como G, Fagnani F, Ozdaglar A (2010) Persistent disagreement in social networks. Working paper Google Scholar
  3. 3.
    Acemoglu D, Bimpikis K, Ozdaglar A (2010) Communication information dynamics in (endogeneous) networks. LIDS report 2813, working paper Google Scholar
  4. 4.
    Acemoglu D, Dahleh M, Lobel I, Ozdaglar A (2010) Heterogeneity and social learning. Working paper Google Scholar
  5. 5.
    Acemoglu D, Dahleh M, Lobel I, Ozdaglar A (2009) Bayesian learning in social networks. LIDS report 2780 Google Scholar
  6. 6.
    Acemoglu D, Chernozhukov V, Yildiz M (2007) Learning and disagreement in an uncertain world. Working paper Google Scholar
  7. 7.
    Aldous D, Fill J (2002) Reversible Markov chains and random walks on graphs. Monograph in preparation. http://www.stat.berkeley.edu/aldous/RWG/book.html
  8. 8.
    Allen B (1981) Generic existence of completely revealing equilibria for economies with uncertainty when prices convey information. Econometrica 49(5):1173–1199 CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Deffuant G, Amblard F, Weisbuch G, Faure T (2002) How can extremism prevail? A study based on the relative agreement interaction model. J Artif Soc Soc Simul 5(4) Google Scholar
  10. 10.
    Bala V, Goyal S (1998) Learning from neighbours. Rev Econ Stud 65(3):595–621 CrossRefzbMATHGoogle Scholar
  11. 11.
    Banerjee A (1992) A simple model of herd behavior. Q J Econ 107:797–817 CrossRefGoogle Scholar
  12. 12.
    Banerjee A, Fudenberg D (2004) Word-of-mouth learning. Games Econ Behav 46:1–22 CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Bikhchandani S, Hirshleifer D, Welch I (1992) A theory of fads, fashion, custom, and cultural change as information cascades. J Polit Econ 100:992–1026 CrossRefGoogle Scholar
  14. 14.
    Binmore K (2008) Rational decisions. Princeton University Press, Princeton Google Scholar
  15. 15.
    Bisin A, Verdier T (2001) The economics of cultural transmission and the dynamics of preferences. J Econ Theory 97(2):298–319 CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Bisin A, Verdier T (2000) Beyond the melting pot: cultural transmission, marriage, and the evolution of ethnic and religious traits. Q J Econ 115(3):955–988 CrossRefGoogle Scholar
  17. 17.
    Blondel VD, Hendrickx JM, Tsitsiklis JN (2009) On Krause’s multi-agent consensus model with state-dependent connectivity. IEEE Trans Autom Control 54(11):2586–2597 CrossRefMathSciNetGoogle Scholar
  18. 18.
    Boyd S, Ghosh A, Prabhakar B, Shah D (2005) Gossip algorithms: design, analysis, and applications. In: Proceedings of IEEE INFOCOM Google Scholar
  19. 19.
    Boyd R, Richerson PJ (1985) Culture and the evolutionary process. The University of Chicago Press, Chicago Google Scholar
  20. 20.
    Cavalli-Sforza LL, Feldman MW (1981) Cultural transmission and evolution: a quantitative approach. Princeton University Press, Princeton Google Scholar
  21. 21.
    Chamley C, Gale D (1994) Information revelation and strategic delay in a model of investment. Econometrica 62:1065–1086 CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Chen Y, Kartik N, Sobel J (2008) Selecting cheap talk equilibria. Econometrica 76(1):117–136 CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Clifford P, Sudbury A (1973) A model for spatial conflict. Biometrika 60:581–588 CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    de Condorcet NC (1785) Essai sur l’application de l’analyse à la probabilite des décisions rendues à la pluralite des voix. Imprimerie Royale, Paris Google Scholar
  25. 25.
    Crawford V, Sobel J (1982) Strategic information transmission. Econometrica 50(6):1431–1451 CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Cripps M, Ely J, Mailath G, Samuelson L (2008) Common learning. Econometrica 76:909–933 CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. Adv Complex Syst 3:87–98 CrossRefGoogle Scholar
  28. 28.
    DeGroot MH, Reaching a consensus. J Am Stat Assoc 69:118–121 Google Scholar
  29. 29.
    DellaVigna S, Kaplan E (2007) The Fox News effect: media bias and voting. Q J Econ 122:1187–1234 CrossRefGoogle Scholar
  30. 30.
    DeMarzo PM, Vayanos D, Zwiebel J (2003) Persuasion bias, social influence, and unidimensional opinions. Q J Econ 118(3):909–968 CrossRefzbMATHGoogle Scholar
  31. 31.
    Ellison G, Fudenberg D (1993) Rules of thumb for social learning. J Polit Econ 101(4):612–643 CrossRefGoogle Scholar
  32. 32.
    Ellison G, Fudenberg D (1995) Word-of-mouth communication and social learning. Q J Econ 110:93–126 CrossRefzbMATHGoogle Scholar
  33. 33.
    Fagnani F, Zampieri S (2008) Randomized consensus algorithms over large scale networks. IEEE J Sel Areas Commun, forthcoming Google Scholar
  34. 34.
    Farrell J, Rabin M (1996) Cheap talk. J Econ Perspect 10(3):103–118 Google Scholar
  35. 35.
    Fortunato S, Stauffer D (2006) Computer simulations of opinions and their reactions to extreme events. In: Albeverio S, Jentsch V, Kantz H (eds) Extreme events in nature and society, 2005. Springer, Berlin Google Scholar
  36. 36.
    Foster D, Vohra RV (1997) Calibrated learning and correlated equilibrium. Games Econ Behav 21:40–55 CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Foster D, Vohra RV (1999) Regret in the online decision problem. Games Econ Behav 29:7–35 CrossRefzbMATHMathSciNetGoogle Scholar
  38. 38.
    Fudenberg D, Levine DK (1998) The theory of learning in games. MIT Press, Cambridge zbMATHGoogle Scholar
  39. 39.
    Fudenberg D, Tirole J (1991) Game theory. MIT Press, Cambridge Google Scholar
  40. 40.
    Gale D, Kariv S (2003) Bayesian learning in social networks. Games Econ Behav 45(2):329–346 CrossRefzbMATHMathSciNetGoogle Scholar
  41. 41.
    Galeotti A, Ghiglino C, Squintani F (2010) Strategic information transmission in networks. Working paper Google Scholar
  42. 42.
    Galton F (1907) Vox populi. Nature 75:450–451 CrossRefGoogle Scholar
  43. 43.
    Gilboa I, Postlewaite A, Schmeidler D (2007) Rationality of belief. Or: why Savage’s axioms are neither necessary nor sufficient for rationality. Working paper Google Scholar
  44. 44.
    Gilboa I, Schmeidler D (1995) Case-based decision theory. Q J Econ 110:605–639 CrossRefzbMATHGoogle Scholar
  45. 45.
    Gilboa I, Schmeidler D (2001) A theory of case-based decisions. Cambridge University Press, Cambridge CrossRefzbMATHGoogle Scholar
  46. 46.
    Gintis H (2009) The bounds of reason: game theory and the unification of the behavioral sciences. Princeton University Press, Princeton zbMATHGoogle Scholar
  47. 47.
    Gladwell M (2000) The tipping point: how little things can make a big difference. Little Brown Google Scholar
  48. 48.
    Glauber RJ (1963) Time-dependent statistics of the Ising model. J Math Phys 4:294–307 CrossRefzbMATHMathSciNetGoogle Scholar
  49. 49.
    Golosov M, Lorenzoni G, Tsyvinski A (2009) Decentralized trading with private information. Working paper Google Scholar
  50. 50.
    Golub B, Jackson MO (2010) How homophily affects diffusion and learning in networks. Unpublished manuscript Google Scholar
  51. 51.
    Golub B, Jackson MO (2007) Naïve learning in social networks and the wisdom of crowds. Am Econ J, Microecon 2(1):112–149 CrossRefGoogle Scholar
  52. 52.
    Grossman SJ (1977) The existence of future markets, and my special expectations and informational externalities. Rev Econ Stud 44(2):431–449 zbMATHGoogle Scholar
  53. 53.
    Grossman S, Stiglitz JE (1980) On the impossibility of informationally efficient markets. Am Econ Rev 70(3):393–408 Google Scholar
  54. 54.
    Gul F (1998) A comment on Aumann’s Bayesian view. Econometrica 66(4):923–927 CrossRefzbMATHMathSciNetGoogle Scholar
  55. 55.
    Hagenbach J, Koessler F (2010) Strategic communication networks. Working paper Google Scholar
  56. 56.
    Hart S, Mas-Colell A (2000) A simple adaptive procedure leading to correlated equilibrium. Econometrica 68(5):1127–1150 CrossRefzbMATHMathSciNetGoogle Scholar
  57. 57.
    Haviv M, Van Der Heyden L (1984) Perturbation bounds for the stationary probabilities of a finite Markov chain. Adv Appl Probab 16(4):804–818 CrossRefzbMATHGoogle Scholar
  58. 58.
    Hayek FA (1945) The use of knowledge in society. Am Econ Rev 35(4):519–530 Google Scholar
  59. 59.
    Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence models, analysis, and simulations. J Artif Soc Soc Simul 5:1–33 Google Scholar
  60. 60.
    Holley R, Liggett TM (1975) Ergodic theorems for weakly interacting systems and the voter model. Ann Probab 3:643–663 CrossRefzbMATHMathSciNetGoogle Scholar
  61. 61.
    Jackson MO (2008) Social and economic networks. Princeton University Press, Princeton zbMATHGoogle Scholar
  62. 62.
    Jadbabaie A, Lin J, Morse S (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001 CrossRefMathSciNetGoogle Scholar
  63. 63.
    Krause U (2000) A discrete nonlinear and nonautonomous model of consensus formation. In: Elaydi S, Ladas G, Popenda J, Rakowski J (eds) Communications in difference equations. Gordon and Breach, Amsterdam Google Scholar
  64. 64.
    Lee I (1993) On the convergence of informational cascades. J Econ Theory 61:395–411 CrossRefzbMATHGoogle Scholar
  65. 65.
    Liggett TM (1985) Interacting particle systems. Springer, New York zbMATHGoogle Scholar
  66. 66.
    Lobel I, Ozdaglar A, Feijer D (2010) Distributed multi-agent optimization with state-dependent communication. LIDS report 2834 Google Scholar
  67. 67.
    Lobel I, Ozdaglar A (2010) Distributed subgradient methods for convex optimization over random networks. LIDS report 2800. IEEE Trans Autom Control, to appear Google Scholar
  68. 68.
    Lorenz J (2005) A stabilization theorem for dynamics of continuous opinions. Physica A 355:217–223 CrossRefMathSciNetGoogle Scholar
  69. 69.
    Mobilia M, Petersen A, Redner S (2007) On the role of zealotry in the voter model. J Stat Mech Theory Exp 128:447–483 zbMATHMathSciNetGoogle Scholar
  70. 70.
    Morgan J, Stocken P (2008) Information aggregation in polls. Am Econ Rev 98(3):864–896 CrossRefGoogle Scholar
  71. 71.
    Nedic A, Ozdaglar A (2009) Distributed subgradient methods for multi-agent optimization. IEEE Trans Autom Control 54(1):48–61 CrossRefMathSciNetGoogle Scholar
  72. 72.
    Olshevsky A, Tsitsiklis JN (2009) Convergence speed in distributed consensus and averaging. SIAM J Control Optim 48(1):33–55 CrossRefzbMATHMathSciNetGoogle Scholar
  73. 73.
    Ostrovsky M (2009) Information aggregation in dynamic markets with strategic traders. Working paper Google Scholar
  74. 74.
    Quine WV (1969) Natural kinds. In: Rescher N (ed) Essays in honor of Carl G. Hempel. Reidel, Dordrecht Google Scholar
  75. 75.
    Radner R (1972) Existence of equilibrium of plans, prices and price expectations in a sequence of markets. Econometrica 40(2):289–303 CrossRefzbMATHMathSciNetGoogle Scholar
  76. 76.
    Radner R (1982) Equilibrium under uncertainty. In: Arrow KJ, Intiligator MD (eds) Handbook of mathematical economics, vol 2. Elsevier, Amsterdam, pp 923–1006 Google Scholar
  77. 77.
    Richerson PJ, Boyd R (2005) Not by genes alone: how culture transformed human evolution. The University of Chicago Press, Chicago Google Scholar
  78. 78.
    Robinson J (1951) An iterative method of solving a game. Ann Math 54:296–301 CrossRefGoogle Scholar
  79. 79.
    Samuelson L (1997) Evolutionary games and equilibrium selection. MIT Press, Cambridge zbMATHGoogle Scholar
  80. 80.
    Sandholm W (2010) Population games and evolutionary dynamics. MIT Press, Cambridge Google Scholar
  81. 81.
    Savage LJ (1954) The foundations of statistics. Wiley, New York zbMATHGoogle Scholar
  82. 82.
    Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57(2):571–587 CrossRefzbMATHMathSciNetGoogle Scholar
  83. 83.
    Schweitzer PJ (1968) Perturbation theory and finite Markov chains. J Appl Probab 5(2):401–413 CrossRefzbMATHMathSciNetGoogle Scholar
  84. 84.
    Simon HA (1957) Models of man. Wiley, New York zbMATHGoogle Scholar
  85. 85.
    Smith L, Sorensen P (1998) Rational social learning with random sampling. Unpublished manuscript Google Scholar
  86. 86.
    Smith L, Sorensen P (2000) Pathological outcomes of observational learning. Econometrica 68(2):371–398 CrossRefzbMATHMathSciNetGoogle Scholar
  87. 87.
    Tahbaz-Salehi A, Jadbabaie A (2008) A necessary and sufficient condition for consensus over random networks. IEEE Trans Autom Control 53(3):791–795 CrossRefMathSciNetGoogle Scholar
  88. 88.
    Tsitsiklis JN (1984) Problems in decentralized decision making and computation. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology Google Scholar
  89. 89.
    Tsitsiklis JN, Bertsekas DP, Athans M (1986) Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans Autom Control 31(9):803–812 CrossRefzbMATHMathSciNetGoogle Scholar
  90. 90.
    Vives X (1997) Learning from others: a welfare analysis. Games Econ Behav 20:177–200 CrossRefzbMATHMathSciNetGoogle Scholar
  91. 91.
    Watts D (2003) Six degrees: the science of a connected age. Norton, New York Google Scholar
  92. 92.
    Weibull J (1995) Evolutionary game theory. MIT Press, Cambridge zbMATHGoogle Scholar
  93. 93.
    Weisbuch G, Kirman A, Herreiner D (2000) Market organization. Economica 110:411–436 Google Scholar
  94. 94.
    Welch I (1992) Sequential sales, learning and cascades. J. Finance 47:695–732 CrossRefGoogle Scholar
  95. 95.
    Wolinsky A (1990) Information revelation in a market with pairwise meetings. Econometrica 58(1):1–23 CrossRefzbMATHMathSciNetGoogle Scholar
  96. 96.
    Wu F, Huberman B (2008) How public opinion forms. In: WINE’ 08 Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of EconomicsMITCambridgeUSA
  2. 2.Laboratory for Information and Decision Systems, Electrical Engineering and Computer Science DepartmentMITCambridgeUSA

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