Once a preferable diversion scheme is selected, the problem of apportioning the gains between the cooperating players still remains, and this is one of the main concerns of this paper.

With the help of game theory, the authors underline that in some cases cooperation may occur without the need of new arrangements, in other cases it is impossible to reach a cooperative solution without new institutional arrangements.

The cooperative game model is developed for Lake Ontario: the _characteristic function_ is derived from data and previous analysis conducted by the authors (and reviewed in a previous sections on water allocation).

The game for the Upper Lakes is quite similar to the Lake Ontario’s and the Core is always non-empty, except for the Lake Michigan-Huron. It was found that if a diversion is to take place from Lake Michigan-Huron, federal government invention will be required since there is no bargaining solution that will benefit all parties. The _Core_ of the game is non-empty. All the results are commented and the authors conclude that in general, more reasonable and equitable solutions were found using the _Nucleolus_ rather than the _Shapley value_ .

Dinar and Wolf (1997) address possible cooperation in the Western Middle East over the Nile water, showing that there is a need to incorporate more politically related considerations on top of the economic and game theory ones. Their thesis is that cooperation among players requires a realization of economic benefits to all players and a meeting of efficiency requirements through economically driven allocations. Cooperation among political (and sometimes hostile) players may not meet these requirements. Political considerations, usually ignored in economic analyses, can hinder or even block possible arrangements.

The paper proposes a framework that includes both economic and political considerations for evaluating transfers or trades of scarce resources. This method quantifies both the economic payoffs using N-person game theory and the political likelihood of any of the coalitions actually forming, using the PRINCE Political Accounting System. The economic-political approach is applied to a case of potential water transfer in the Western Middle East. Results suggest that incorporating political considerations in the analysis stabilizes the regional solution suggested by economic-related allocations.

A _Political Accounting System_ (PAS) to quantitatively and qualitatively predict interactions among players is also used in the political science literature. The PAS assumes that the political impact of players on joint decisions be affected by three factors: issue position, power, and salience. The first element of this system is the _issue position_ , expressing the strength of each participant’s position for or against each of the issues. A second element is the _power_ of a player to influence an issue, the third element is _salience_ , i.e. the importance each player attaches to a particular issue.

Two problems may affect the application of the PAS approach: first the measure of values to be included in the PAS is, in many cases, subjective, ordinal, and possibly inconsistent, second this approach does not consider coalitional arrangements among the players.

The authors consider a regional allocation game, where a water resource has to be shared, as well as monetary compensations and exchange of technologies for water, under certain arrangements, among different users in the region.

The _Core_ , the _Shapley value_ and the _Generalized Shapley value_ are considered, and a PAS is included in the model, to calculate political probabilities for the formation of different coalitions. (The _PRINCE_ Political Accounting System, developed by Coplin and O’Leary (1974, 1976, 1983) is used in this paper.) The combined game theory and PAS approach has been applied to a case of water transfer in the Western Middle East. The involved players are Egypt, Israel, the Gaza Strip and the West Bank. The values assigned to the political components of the PAS in this paper are the best quantitative assessment of an elusive quantity. The authors recognize the need to develop more objective measures for each component of political viability.

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