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The Journal of Mathematical Sociology Volume 17, 1992 - Issue 2-3
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Original Articles

Stability and monotonicity for interactive Markov chains

John Conlisk University of California San Diego, La Jolla, CA, 92093
Pages 127-143 | Received 14 Apr 1991, Published online: 26 Aug 2010

References

  • Bartholomew , D. J. 1982 . Stochastic models for social processes, , 3rd edition , New York : John Wiley & Sons .
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  • Brumelle , S. L. and Gerchak , Y. 1980 . A stochastic model allowing interaction among individuals and its behavior for large populations . Journal of Mathematical Sociology , 7 : 73 – 90 .
  • Conlisk , J. 1976 . Interactive Markov chains . Journal of Mathematical Sociology , 4 : 157 – 185 .
  • Conlisk , J. 1978 . A stability theorem for an interactive Markov chain . Journal of Mathematical Sociology , 6 : 163 – 168 .
  • Conlisk , J. 1982 . The law of supply and demand as a law of Markov chains . Journal of Economic Theory , 26 : 1 – 16 .
  • Conlisk , J. 1990 . Monotone mobility matrices . Journal of Mathematical Sociology , 15 : 173 – 191 .
  • Fujimoto , T. and Krause , U. 1988 . Asymptotic properties for inhomogeneous iterations of nonlinear operators . SLAM Journal of Mathematical Analysis , 19 : 841 – 853 .
  • Gerchak , Y. 1983 . On interactive chains with finite populations . Journal of Mathematical Sociology , 9 : 255 – 258 .
  • Keilson , J. and Kester , A. 1977 . Monotone matrices and monotone Markov chains . Stochastic Processes and Tlieir Applications , 5 : 231 – 241 .
  • Krause , U. 1986 . Perron's stability theorem for non‐linear mappings . Journal of Mathematical Economics , 15 : 275 – 282 .
  • Lehoczky , J. P. 1980 . Approximations for interactive Markov chains in discrete and continuous time . Journal of Mathematical Sociology , 7 : 139 – 157 .
  • Matras , J. 1967 . Social mobility and social structure: Some insights from the linear model . American Sociological Review , 32 : 608 – 614 .

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