On the Size and Structure of Group Cooperation

40 Pages Posted: 23 Oct 2002

See all articles by Matthew Haag

Matthew Haag

University of Warwick - Department of Economics

Roger Lagunoff

Georgetown University - Department of Economics

Date Written: June 2003

Abstract

This paper examines characteristics of cooperative behavior in a repeated, n-person, continuous action generalization of a Prisoner' 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' 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.

Keywords: Repeated Games, Maximal Average Cooperation Likelihood, Heterogeneous Discount Factors, Returns to Scale

JEL Classification: C7, D62, D7

Suggested Citation

Haag, Matthew and Lagunoff, Roger, On the Size and Structure of Group Cooperation (June 2003). Available at SSRN: https://ssrn.com/abstract=335160 or http://dx.doi.org/10.2139/ssrn.335160

Matthew Haag (Contact Author)

University of Warwick - Department of Economics ( email )

Coventry CV4 7AL
United Kingdom

Roger Lagunoff

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States
202-687-1510 (Phone)
202-687-6102 (Fax)