This paper considers environments in which several agents (countries, farmers, cities) share water from a river. Each agent enjoys a concave benefit function from consuming water up to a satiation level. Noncooperative extraction is typically inefficient and any group of agents can gain if they agree on how to allocate water with monetary compensations. The paper describes which allocations of water and money are acceptable to riparian agents according to core stability and several criteria of fairness. It reviews some theoretical results. It then discusses the implementation of the proposed allocation with negotiation rules and in water markets. Lastly, it provides some policy insights.