Sharing a river

CAHIER 08-2000

SHARING A RIVER

Stefan AMBEC and Yves SPRUMONT Université de Montréal Centre de recherche et développement en économique C.P. 6128, Succursale Centre-ville Montréal (Québec) H3C 3J7 Téléphone : (514) 343-6557 Télécopieur : (514) 343-5831 Université de Montréal Centre de recherche et développement en économique C.P. 6128, Succursale Centre-ville Montréal (Québec) H3C 3J7 Téléphone : (514) 343-6557 Télécopieur : (514) 343-5831

CAHIER 08-2000

SHARING A RIVER

Stefan AMBEC1 and Yves SPRUMONT2

1

GREEN, Université Laval

2

Centre de recherche et développement en économique (C.R.D.E.) and Département de sciences économiques, Université de Montréal

May 2000

__________________

The authors would like to thank E. Edmonds and M. Truchon for very useful comments. Ambec's research was supported by the C.R.D.E., CIRANO, and GREEN. Sprumont acknowledges financial support from the Social Sciences and Humanities Research Council (SSHRC) of Canada.

RÉSUMÉ

Un groupe d'agents doit partager l'eau d'un fleuve le long duquel il est situé. Les compensations monétaires sont autorisées. Nous montrons que le jeu coopératif associé à ce problème de partage est convexe : son noyau est donc grand et facile à décrire. Nous proposons le critère d'équité suivant : aucun groupe d'agents ne devrait obtenir un bien-être supérieur à celui qu'il pourrait atteindre en l'absence des autres. Nous montrons qu'une seule distribution dans le noyau satisfait ce critère.

Mots clés : propriété commune, équité, noyau

ABSTRACT

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. We are interested in efficiency, stability (in the sense of the core), and fairness (in a sense to be defined). We first show that the cooperative game associated with our problem is convex : its core is therefore large and easily described. Next, we propose the following fairness requirement : no group of agents should enjoy a welfare higher than what it could achieve in the absence of the remaining agents. We prove that only one welfare vector in the core satisfies this condition : it is the marginal contribution vector corresponding to the ordering of the agents along the river. We discuss how it could be decentralized or implemented.

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