Asymptotics of a matrix valued Markov chain arising in sociology

Stochastic Processes and their Applications

Volumn 104, Issue 1, 2003, Pages 155-171

  Bonacich, Phillip ^a   Liggett, Thomas M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Exchange networks; Markov chains; Randomly chosen maps; Reciprocity

Indexed keywords

EID: 0037361195     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(02)00231-4     Document Type: Article

References (11)

1. Blau, P., 1967. Exchange and Power in Social Life. Wiley, New York.
2. Bonacich, P., 1998. An algebraic theory of strong power in negatively connected exchange networks. J. Math. Sociol. 23, 203-224.
3. Burton, R.M., Keller, G., 1993. Stationary measures for randomly chosen maps. J. Theoret. Probab. 6, 1-16.
4. Bush, R.R., Mosteller, F., 1955. Stochastic Models for Learning. Wiley, New York.
5. Cook, K.S., Emerson, R.M., Gillmore, M.R., Yamagishi, T., 1983. The distribution of power in exchange networks: theory and experimental results. Amer. J. Sociol. 89, 275-305.
6. Durrett, R., 1996. Probability: Theory and Examples, 2nd Edition. Duxbury, Belmont, CA.
7. Iosifescu, M., Grigorescu, S., 1990. Dependence with Complete Connections and its Applications. Cambridge University Press, Cambridge.
8. Markovsky, B., Skvoretz, J., Willer, D., Lovaglia, M., Erger, J., 1993. The seeds of weak power: an extension of network exchange theory. Amer. Sociol. Rev. 58, 197-209.
9. Molm, L., Peterson, G., Takahashi, N., 1999. Power in negotiated and reciprocal exchange networks. Amer. Sociol. Rev. 64, 876-890.
10. Molm, L., Takahashi, N., Peterson, G., 2000. Risk and trust in social exchange: an experimental test of a classic proposition. Amer. J. Sociol. 105, 1396-1427.
11. Pemantle, R., Skyrms, B., 2000. A dynamic model of social network formation. Proc. Nat. Acad. Sci. 97, 9340-9346.