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An infinite stochastic model of social network formation

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  • Liggett, Thomas M.
  • Rolles, Silke W. W.

Abstract

We consider an infinite interacting particle system in which individuals choose neighbors according to evolving sets of probabilities. If x chooses y at some time, the effect is to increase the probability that y chooses x at later times. We characterize the extremal invariant measures for this process. In an extremal equilibrium, the set of individuals is partitioned into finite sets called stars, each of which includes a "center" that is always chosen by the other individuals in that set.

Suggested Citation

  • Liggett, Thomas M. & Rolles, Silke W. W., 2004. "An infinite stochastic model of social network formation," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 65-80, September.
    • Handle: RePEc:eee:spapps:v:113:y:2004:i:1:p:65-80
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    References listed on IDEAS

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    1. Pemantle, Robin & Skyrms, Brian, 2004. "Time to absorption in discounted reinforcement models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 1-12, January.
    2. Bonacich, Phillip & Liggett, Thomas M., 2003. "Asymptotics of a matrix valued Markov chain arising in sociology," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 155-171, March.
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    Cited by:

    1. Gunter M. Schutz & Fernando Pigeard de Almeida Prado & Rosemary J. Harris & Vladimir Belitsky, 2007. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Papers 0801.0003, arXiv.org, revised Jun 2009.
    2. Schütz, Gunter M. & de Almeida Prado, Fernando Pigeard & Harris, Rosemary J. & Belitsky, Vladimir, 2009. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4126-4144.

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