Abstract
The use of water in the Jordan Basin has been a key factor in the conflict between Israel and the Palestinians, and among Israel and its neighbours. In this paper, we explore possible ways of sharing water through a negotiation game with two players—Arabs and Israelis. We estimate a set of optimum Pareto allocations, as well as identifying a range of negotiated solutions. Our results suggest that viable solutions would improve incomes by some 20% compared to the current status quo. These solutions are close to the long-standing proposal contained in the Johnston Plan. Meanwhile, theoretical fairness criteria, which are more favourable to the Arabs than the Johnston Plan, maybe are not actually better in technical terms and could in any case only be achieved if the Arabs’ negotiating position were much stronger than the Israelis’.
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Appendix
Appendix
Regular Nash bargaining solutions with break-off points (ω I ;ω A )≠(0;0)
Let us find the negotiating solutions to the problem:
where R=(ω I ;ω A )≠(0;0) is the break-off point. This problem will be resolved for three cases, namely: R3=(254.35;430.25), R4=(424.89;337.54) and R5=(568.72;195.57). These break-off points are the utilities that each player would obtain if breaking off the game would ensure only half of the utility of fairness criterion F2 (contribution of each country to flows in the basin), the Johnston Plan and criterion F4 (current uses), all three of which could serve as the basis for an actual negotiation scenario. The solutions, which we shall call S3, S4 and S5, are the efficient points
S3 is the best outcome for the Arabs and S5 the worst. Solution S3 is somewhat better for the Arabs than JP, but significantly worse than the fair situation, F2, with regard to which the break-off point is defined. In comparison with F2, the best outcome for Israel is Nash solution S3.
Nash solution S4 is very close to solution JP, used as the benchmark to define break-off. Finally, S5 improves the conditions of the fairness criterion F4 but is still a fairly long way from JP.
Figure 4 shows the break-off points R3, R4 and R5 and S3, S4 and S5 respectively.
Generalized nash bargaining solutions
The generalized or asymmetric Nash bargaining problem would be as follows:
It can easily be seen on an isoquant that the target function verifies:
This demonstrates that α I and α A are indicators of negotiating strength or power, as the greater (less) exponent α I may be, the more favourable (unfavourable) the exchange will be for Israel.
For reasons of brevity, we shall look only at general solutions with break-off points at R=(0;0) and certain values of α I and α A . We have obtained the 11 general Nash solutions shown below by direct calculation. These may be compared with the regular solution obtained above.
Greater Arab negotiating power
Greater Israeli negotiating power
As might have been expected, the players increase their gains where they have greater negotiating power. The generalized Nash solutions in which the Arabs have greater negotiating power (SA2, SA3, SA4, SA5, SA6 and SA9) are situated increasingly to the left of S1. In contrast, the generalized solutions that are favourable to Israel (SI2, SI3, SI4 and SI5) are at some distance to the right of S1. We may note here that certain solutions based on a specific negotiating power may coincide approximately with the allocation of some of the fair allocation factors. See Figure 4.
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Atwi, M., Chóliz, J. A negotiated solution for the Jordan Basin. J Oper Res Soc 62, 81–91 (2011). https://doi.org/10.1057/jors.2009.162
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DOI: https://doi.org/10.1057/jors.2009.162