Time to absorption in discounted reinforcement models
Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in which the past is exponentially discounted or forgotten. Often, models in this subclass have the property of becoming trapped with probability 1 in some degenerate state. While previous work has concentrated on such limit results, we concentrate here on a contrary effect, namely that the time to become trapped may increase exponentially in 1/x as the discount rate, 1-x, approaches 1. As a result, the time to become trapped may easily exceed the lifetime of the simulation or of the physical data being modeled. In such a case, the quasi-stationary behavior is more germane. We apply our results to a model of social network formation based on ternary (three-person) interactions with uniform positive reinforcement.
Volume (Year): 109 (2004)
Issue (Month): 1 (January)
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- A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 13(3), pages 547-560, 02.
- Fudenberg, D. & Kreps, D.M., 1992.
"Learning Mixed Equilibria,"
92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
- Glen Ellison, 2010.
"Learning, Local Interaction, and Coordination,"
Levine's Working Paper Archive
391, David K. Levine.
- Anderlini, L. & Ianni, A., 1996. "Learning on a Torus," Discussion Paper Series In Economics And Econometrics 9611, Economics Division, School of Social Sciences, University of Southampton.
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