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The Egalitarian Allocation (EA) is a well-known profit sharing method forcooperative games which attempts to distribute profit among participants in amost equal way while respecting the individual contributions to the obtainedprofit. Despite having desirable properties from the viewpoint of game theorylike being contained in the core, the EA is in general hard to compute. Anotherwell-known method is given by Vickrey Payments (VP). Again, the VP havedesirable properties like coalitional rationality, the VP do not fulfill budgetbalance in general and, thus, are not contained in the core in general. Oneattempt to overcome this shortcoming is to scale down the VP. This can be doneby a unique scaling factor, or, by individual scaling factors. Now, theindividual scaled Vickrey Payments (ISV) are computed by maximizing the scalingfactors lexicographically. In this paper we show that the ISV payments are infact identical to a weighted EA, thus exhibiting an interesting connectionbetween EA and VP. With this, we conclude the uniqueness of the ISV paymentsand provide a polynomial time algorithm for computing a special weighted EA.

On the Connection between Individual Scaled Vickrey Payments and the Egalitarian Allocation