On the size and structure of group cooperation

• 成果类型: Article
• 署名作者: Haag, Matthew; Lagunoff, Roger
• 署名单位: Georgetown University; University of Warwick
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2005.08.011
• 发表日期: 2007
• 页码: 68-89
• 关键词: Repeated games; maximal average cooperation; heterogeneous discount factors; Returns to scale

摘要

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? This paper examines characteristics of cooperative behavior in the class of symmetric, repeated games of collective action. These are games characterized by free rider problems in the level of cooperation achieved. The Repeated Prisoner's Dilemma games is a special case. We characterize the level of maximal average cooperation (MAC), the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, that the group can achieve. The MAC 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, in a class of Prisoner's Dilemma games, we show under weak conditions that the MAC exhibits increasing returns to scale in a range of heterogeneous discount factors. That is, larger groups are more cooperative, on average, than smaller ones. By contrast, when the group has a common discount factor, the MAC is invariant to group size. (c) 2006 Elsevier Inc. All rights reserved.