Imitation and Efficient Contagion

Boyer, Tristan and Jonard, Nicolas (2010): Imitation and Efficient Contagion.

Abstract

In this paper we study the conditions under which efficient behavior can spread from a finite initial seed group to an infinite population living on a network. We formulate conditions on payoffs and network structure under which overall contagion occurs in arbitrary regular networks. Central in this process is the communication pattern among players who are confronted with the same decision, i.e. who are at the same distance from the initial seed group. The extent to which these agents interact among themselves (rather than with players who already have faced or subsequently will face the decision problem) is critical in the Prisoner’s Dilemma. In the Coordination Game the key element is the cohesion of the efficient cluster, a property which is different from the one identified in the Prisoner’s Dilemma. Additional results are obtained when we distinguish the interaction and information neighborhoods. Specifically, we find that contagion tends to be favored by fast neighborhood growth if an assumption of conservative behavior is made. We discuss our findings in relation to the notions of clustering, transitivity and cohesion.

• Item Type: MPRA Paper
• Language: English
• Keywords: imitation, contagion, regular graphs, local interaction game
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

G. Abramson and M. Kuperman, Social games in a social network, Physical Review E 63 (2001), no. 3, 30901.

C. Alós-Ferrer and S. Weidenholzer, Contagion and efficiency, Journal of Economic Theory 143 (2008), no. 1, 251–274.

L. Anderlini and A. Ianni, The dynamics of norms, ch. Learning on a torus., pp. 87–107, Cambridge University Press, 1997.

J. Apesteguia, S. Huck, and J. Oechssler, Imitation–theory and experimental evidence, Journal of Economic Theory 136 (2007), no. 1, 217–235.

J. Bergin and D. Bernhardt, Cooperation through imitation, Games and Economic Behavior 67 (2009), no. 2, 376–388.

J. Bergin and B.L. Lipman, Evolution with state-dependent mutations, Econometrica 64 (1996), no. 4, 943–956.

S.K. Berninghaus and U. Schwalbe, Evolution, interaction, and nash equilibria, Journal of Economic Behavior and Organization 29 (1996), no. 1, 57–85.

K. Binmore and L. Samuelson, Muddling through, noisy equilibrium selection, Journal of Economic Theory 74 (1997), 235–265.

L.E. Blume, The statistical mechanics of strategic interaction, Games and Economic Behavior 5 (1993), 387–424.

L.E. Blume, The statistical mechanics of best-response strategy revision, Games and Economic Behavior 11 (1995), no. 2, 111–145.

E.J. Cartwright, Contagion and the speed of adjustment in small worlds., International Game Theory Review 9 (2007), no. 4, 689–704.

P. Duersch, A. Kolb, J. Oechssler, and B.C. Schipper, Rage against the machines: how subjects play against learning algorithms., Economic Theory 43 (2010), no. 3, 407–430.

J. Durieu, H. Haller, and P. Solal, Cognitive economics: New trends, ch. Contagion and Dominating Sets, pp. 135–152, Emerald Group Pub Ltd, 2007.

G. Ellison, Learning, local interaction and cooperation, Econometrica 61 (1993), 1047–1071.

G. Ellison, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Review of Economic Studies 67 (2000), no. 1, 17–45. 12

I. Eshel, L. Samuelson, and A. Shaked, Altruists, egoists, and hooligans in a local interaction model, American Economic Review 88 (1998), 157–179.

I. Eshel, E. Sansone, and A. Shaked, The emergence of kinship behavior in structured populations of unrelated individuals, International Journal of Game Theory 28 (1999), no. 4, 447–463.

B.A. Huberman and N.S. Glance, Evolutionary games and computer simulations, Proceedings of the National Academy of Sciences 90 (1993), no. 16, 7716–7718.

T. Jun and R. Sethi, Neighborhood structure and the evolution of cooperation, Journal of Evolutionary Economics 17 (2007), no. 5, 623–646.

M. Kandori, G.J. Mailath, and R. Rob, Learning, mutation, and long run equilibria in games, Econometrica 61 (1993), 29–56.

M.B. Lieberman and S. Asaba, Why do firms imitate each other?, Academy of Management Review 31 (2006), no. 2, 366–385.

D. López-Pintado, Contagion and coordination in random networks, International Journal of Game Theory 34 (2006), no. 3, 371–381.

F. Mengel, Conformism and cooperation in a local interaction model, Journal of Evolutionary Economics 19 (2009), no. 3, 397–415.

S. Morris, Contagion, Review of Economic Studies (2000), 57–78.

M.A. Nowak, S. Bonhoeffer, and R.M. May, Spatial games and the maintenance of cooperation, Proceedings of the National Academy of Sciences 91 (1994), no. 11, 4877–4881.

M.A. Nowak and R.M. May, Evolutionary games and spatial chaos, Nature 359 (1992), no. 6398, 826–829.

M.A. Nowak and R.M. May, The spatial dilemmas of evolution, International Journal of Bifurcation and Chaos 3 (1993), 35–35.

H. Ohtsuki, C. Hauert, E. Lieberman, and M.A. Nowak, A simple rule for the evolution of cooperation on graphs and social networks, Nature 441 (2006), 502–505.

A.V. Outkin, Cooperation and local interactions in the prisoners’ dilemma game, Journal of Economic Behavior and Organization 52 (2003), no. 4, 481–503.

M. Pingle and R.H. Day, Modes of economizing behavior: Experimental evidence, Journal of Economic Behavior and Organization 29 (1996), no. 2, 191–209.

A.J. Robson and F. Vega-Redondo, Efficient equilibrium selection in evolutionary games with random matching, Journal of Economic Theory, 70 (1996), no. 1, 65–92.

C.P. Roca, J.A. Cuesta, and A. Sánchez, Effect of spatial structure on the evolution of cooperation, Physical Review E 80 (2009), no. 4, 46106.

L. Samuelson, Evolutionary games and equilibrium selection, Mit Press, 1997.

K.H. Schlag, Why imitate, and if so, how? a bounded rationality approach to multi-armed bandits, Journal of Economic Theory 78 (1998), 130–156.

H.A. Simon, A behavioral model of rational choice, The Quarterly Journal of Economics 69 (1955), no. 1, 99–118.

F. Vega-Redondo, M. Marsili, and F. Slanina, Clustering, cooperation, and search in social networks., Journal of the European Economic, Association 3 (2005), no. 2/3, 628–638.

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

H.P. Young, Individual strategy and social structure: An evolutionary theory of institutions, Princeton University Press, 1998.