Learning and convergence in networks
We study the convergence properties of learning in social and economic networks. We characterize the effect of network structure on the long-run convergent behaviour and on the time of convergence to steady state. Agents play a repeated game governed by two underlying behavioural rules; they are myopic and boundedly rational. Under this setup, the long-run limit of the adoptive process converges to a unique equilibrium. We treat the dynamic process as a Markov chain and derive the bound for the convergence time of the chain in terms of the stationary distribution of the initial and steady state population configurations, and the spectrum of the transition matrix. We in turn differentiate between the two antagonistic effects of the topology of the interaction structure on the convergence time; that through the initial state and that through the asymptotic behaviour. The effect through the initial state favours local interactions and sparsely connected network structures, while that through the asymptotic behaviour favours densely and uniformly connected network structures. The main result is that the most efficient network topologies for faster convergence or learning are those where agents belong to subgroups in which the inter-subgroup interactions are "weaker" relative to within subgroup interactions. We further show that the inter-subgroup interactions or long-ties should not be "too weak" lest the convergence time be infinitely long and hence slow learning.
|Date of creation:||2012|
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- Charles F. Manski, 2000.
"Economic Analysis of Social Interactions,"
Journal of Economic Perspectives,
American Economic Association, vol. 14(3), pages 115-136, Summer.
- Bala, Venkatesh & Goyal, Sanjeev, 1998.
"Learning from Neighbours,"
Review of Economic Studies,
Wiley Blackwell, vol. 65(3), pages 595-621, July.
- Mariagiovanna Baccara & Leeat Yariv, 2008.
"Similarity and Polarization in Groups,"
08-27, New York University, Leonard N. Stern School of Business, Department of Economics.
- M. Kandori & G. Mailath & R. Rob, 1999.
"Learning, Mutation and Long Run Equilibria in Games,"
Levine's Working Paper Archive
500, David K. Levine.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
- Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
- BERGIN, James & LIPMAN, Bart, 1994.
"Evolution with State-Dependent Mutations,"
CORE Discussion Papers
1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Aderlini, L. & Ianni, A., 1993.
"Path Dependence and Learning from Neighbours,"
186, Cambridge - Risk, Information & Quantity Signals.
- Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
- John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
- Brock,W.A. & Durlauf,S.N., 2000.
"Discrete choice with social interactions,"
7, Wisconsin Madison - Social Systems.
- Chwe, Michael Suk-Young, 2000. "Communication and Coordination in Social Networks," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 1-16, January.
- Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
- Ellison, Glenn, 1993.
"Learning, Local Interaction, and Coordination,"
Econometric Society, vol. 61(5), pages 1047-71, September.
- Martin Ruef, 2002. "Strong ties, weak ties and islands: structural and cultural predictors of organizational innovation," Industrial and Corporate Change, Oxford University Press, vol. 11(3), pages 427-449, June.
- Blume Lawrence E., 1993.
"The Statistical Mechanics of Strategic Interaction,"
Games and Economic Behavior,
Elsevier, vol. 5(3), pages 387-424, July.
- L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
- Yannis Ioannides, 2001.
"Topologies of Social Interactions,"
Discussion Papers Series, Department of Economics, Tufts University
0104, Department of Economics, Tufts University.
- Yannis M. Ioannides, 2004. "Topologies Of Social Interactions," Econometric Society 2004 North American Winter Meetings 287, Econometric Society.
- Arthur, W. Brian & Lane, David A., 1993. "Information contagion," Structural Change and Economic Dynamics, Elsevier, vol. 4(1), pages 81-104, June.
- Lawrence Blume, 1993.
"The Statistical Mechanics of Best-Response Strategy Revision,"
Game Theory and Information
9307001, EconWPA, revised 26 Jan 1994.
- Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
- Daron Acemoglu & Munther A. Dahleh & Ilan Lobel & Asuman Ozdaglar, 2008.
"Bayesian Learning in Social Networks,"
NBER Working Papers
14040, National Bureau of Economic Research, Inc.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- Young, H Peyton, 1998. "Conventional Contracts," Review of Economic Studies, Wiley Blackwell, vol. 65(4), pages 773-92, October.
- H. Peyton Young, 1996. "The Economics of Convention," Journal of Economic Perspectives, American Economic Association, vol. 10(2), pages 105-122, Spring.
- Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-40, June.
- A. Bassanini & G. Dosi, 1998. "Competing Technologies, International Diffusion and the Rate of Convergence to a Stable Market Structure," Working Papers ir98012, International Institute for Applied Systems Analysis.
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