On the size and structure of group cooperation
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 (No.650).
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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|
|Official Date:||29 September 2002|
|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|Status:||Not Peer Reviewed|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)|
 Aoyagi, M. (1996), “Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games,” Journal of Economic Theory, 71:378-93.
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