Social Learning and the Shadow of the Past

Heller, Yuval and Mohlin, Erik (2017): Social Learning and the Shadow of the Past. Forthcoming in: Journal of Economic Theory No. forthcoming

Abstract

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact.

• Item Type: MPRA Paper
• Language: English
• Keywords: Social learning, steady state, path dependence.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness

References

Acemoglu, Daron, Dahleh, Munther A., Lobel, Ilan, & Ozdaglar, Asuman. 2011. Bayesian learning in social networks. The Review of Economic Studies, 78(4), 1201–1236.

Arthur, W. Brian. 1989. Competing technologies, increasing returns, and lock-in by historical events. The economic journal, 99(394), 116–131.

Arthur, W. Brian. 1994. Increasing returns and path dependence in the economy. University of michigan Press.

Banerjee, Abhijit, & Fudenberg, Drew. 2004. Word-of-mouth learning. Games and Economic Behavior, 46(1), 1–22.

Cason, Timothy N., Friedman, Daniel, & Hopkins, Ed. 2014. Cycles and instability in a rock–paper–scissors population game: A continuous time experiment. The Review of Economic Studies, 81(1), 112–136.

Ellison, Glenn, & Fudenberg, Drew. 1993. Rules of thumb for social learning. Journal of Political Economy, 101, 612–643.

Ellison, Glenn, & Fudenberg, Drew. 1995. Word-of-mouth communication and social learning. The Quarterly Journal of Economics, 110(1), 93–125.

Foster, Dean, & Young, Peyton. 1990. Stochastic evolutionary game dynamics. Theoretical Population Biology, 38(2), 219–232.

Heller, Yuval, & Mohlin, Erik. 2017. Observations on Cooperation. Mimeo.

Kandori, Michihiro, Mailath, George J., & Rob, Rafael. 1993. Learning, mutation, and long run equilibria in games. Econometrica, 61(1), 29–56.

Kaniovski, Yuri M., & Young, H. Peyton. 1995. Learning dynamics in games with stochastic perturbations. Games and Economic Behavior, 11(2), 330–363.

Munkres, James R. 2000. Topology. 2nd edn. Prentice Hall. Munshi, Kaivan. 2004. Social learning in a heterogeneous population: technology diffusion in the Indian Green Revolution. Journal of development Economics, 73(1), 185–213.

Nowak, Martin A., & Sigmund, Karl. 1998. Evolution of indirect reciprocity by image scoring. Nature, 393(6685), 573–577.

Okuno-Fujiwara, Masahiro, & Postlewaite, Andrew. 1995. Social norms and random matching games. Games and Economic Behavior, 9(1), 79–109.

Oyama, Daisuke, Sandholm, William H., & Tercieux, Olivier. 2015. Sampling best response dynamics and deterministic equilibrium selection. Theoretical Economics, 10(1), 243–281.

Pata, Vittorino. 2014. Fixed point theorems and applications. Mimeo.

Phelan, Christopher, & Skrzypacz, Andrzej. 2006. Private monitoring with infinite histories. Tech. rept. Federal Reserve Bank of Minneapolis.

Rosenthal, Robert W. 1979. Sequences of games with varying opponents. Econometrica, 47(6), 1353–1366.

Sandholm, William H. 2001. Almost global convergence to p-dominant equilibrium. International Journal of Game Theory, 30(1), 107–116.

Sandholm, William H. 2011. Population Games and Evolutionary Dynamics. Cambridge, MA: MIT Press.

Takahashi, Satoru. 2010. Community enforcement when players observe partners’ past play. Journal of Economic Theory, 145(1), 42–62.

Young, H. Peyton. 1993a. The evolution of conventions. Econometrica, 61(1), 57–84.

Young, H. Peyton. 1993b. An evolutionary model of bargaining. Journal of Economic Theory, 59(1), 145–168.

Young, H. Peyton. 2015. The evolution of social norms. Annual Reviews of Economics, 7(1), 359–387.