COMMON POOL GAMES ARE CONVEX GAMES HOLGER MEINHARDT Institute of Statistics and Economic Theory University of Karlsruhe Abstract For the class of cooperative common pool games the paper focuses on the question of how, during the preplay negotiation process, the ability of coalitions to enforce their claims imposes external- ities on the opposition by having an impact on the jointly pro- duced resource. One of our main results is that common pool games are clear games. Based on this result we are able to derive sufficient conditions for the convexity of the characteristic func- tion, which establishes the second main result in the paper, namely that cooperative common pool games are characterized by increas- ing returns with respect to the coalition size. 1. Introduction In commons situations, such as fishing grounds and groundwater basins, agents jointly manage a resource where the exploitation by one user restricts the consumption by or production opportunities of other users. In these situations we observe rivalry in the yield. In general, it is not possible to exclude anyone from the use of the jointly managed resource because of its prohibitive costs. Public goods are not excludable and in contrast to common pool resources their yield is nonrivalrous. In the former case the self-interests of the rational agents imply a unilateral increase in their investment to improve their own returns on the com- mons, with the consequence of a reduction in the average return of all other appropriators, thereby imposing externalities. One would expect by Holger Meinhardt, Institute of Statistics and Economic Theory, University of Karlsruhe, P.O. Box 69 80, Zirkel 2, D-76128 Karlsruhe, Germany ~holger@iwb.uni-sb.de; hme@- vwl3sun1.wiwi.uni-karlsruhe.de! . The author is indebted to Axel Ostmann for helpful comments and suggestions. The author also thanks Th. Driessen, Martha Saboya Baquero, and an anonymous referee for useful comments and proposals. The usual disclaimer applies. Research was supported by the Deutsche Forschungs gemeinschaft. Received 10 March 1998; Accepted 7 September 1998. © 1999 Blackwell Publishers, Inc. Journal of Public Economic Theory,1 ~2! , 1999, pp. 247–270. 247