Haag, Matthew and Lagunoff, Roger Dean (2002) On the size and structure of group cooperation. Working Paper. Coventry: University of Warwick, Department of Economics. (Warwick economic research papers.

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Abstract

This paper examines characteristics of cooperative behavior in a repeated, n-person, continuous action generalization of a Prisoner’s Dilemma game. When time preferences are heterogeneous and bounded away from one, how “much” cooperation can be achieved by an ongoing group? How does group cooperation vary with the group’s size and structure? For an arbitrary distribution of discount factors, we characterize the maximal average co-operation (MAC) likelihood of this game. The MAC likelihood is the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, that the group can achieve. The MAC likelihood is shown to be increasing in monotone shifts, and decreasing in mean preserving spreads, of the distribution of discount factors. The latter suggests that more heterogeneous groups are less cooperative on average. Finally, we establish weak conditions under which the MAC likelihood exhibits increasing returns to scale when discounting is heterogeneous. That is, larger groups are more cooperative, on average, than smaller ones. By contrast, when the group has a common discount factor, the MAC likelihood is invariant to group size.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Prisoner's dilemma game, Maximal functions, Cooperation, Externalities (Economics), Game theory
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	29 September 2002
Number:	No.650
Number of Pages:	33
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	National Science Foundation (U.S.) (NSF)
Grant number:	SES-0108932 (NSF)
References:	[1] Aoyagi, M. (1996), “Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games,” Journal of Economic Theory, 71:378-93. [2] Celentani, M., D Fudenberg, D. Levine, and W. Pesendorfer (1995), “Maintaining a Reputation against a Long-lived Opponent,” Econometrica, 64:691-704. [3] Fudenberg D., and D. Levine (1989), “Reputation and Equilibrium Selection in Games with a Patient Player,” Econometrica, 57:759-78. [4] Fudenberg, D. and E. Maskin (1986), “The Folk Theorem in Repeated Games with Discounting or with Incomplete Information,” Econometrica, 54: 533-56. [5] Fudenberg, D., D. Kreps, and E. Maskin (1990), “Repeated Games with Long-run and Short-run Players,” Review of Economic Studies, 57: 555-73. [6] Harrington, J. (1989), “Collusion Among Asymmetric Firms: The Case of Different Discount Factors, International Journal of Industrial Organization, 7: 289-307. [7] Haag, M. and R. Lagunoff (2001), “Social Norms, Local Interaction, and Neighborhood Planning,” mimeo. [8] Lehrer, E. and A. Pauzner (1999), “Repeated Games with Differential Time Preferences,” Econometrica, 67: 393-412. [9] Olson, Mancur (1965), The Logic of Collective Action, Cambridge: Harvard University Press.
URI:	http://wrap.warwick.ac.uk/id/eprint/1537

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