M.Sc Student | Tangir Yoav |
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Subject | The d-Player Partition Bargaining Problem |

Department | Department of Industrial Engineering and Management |

Supervisor | Mr. Uriel Rothblum (Deceased) |

The *partition bargaining problem* concerns a model
where *n* items are partitioned among *d* players, with each player
associating a positive (additive) utility with each item. A *partition* of
the items to the players is then associated with a corresponding *d*-dimensional
utility vector in *R ^{d}*. Consequently, lotteries over partitions
are also associated with the

Our approach is to enumerate the partitions associated with vectors on the Pareto-optimal surface of the partition polytope. In addition, we study properties of lotteries over Pareto-optimal partitions. It is shown that, there is only one item to be randomized between each couple of players, in a lottery whose expected utility is Pareto-optimal. In all, the assignment of most items under such lotteries is deterministic, while a limited set of at most d(d-1)/2 items is to be randomized among the players. In particular, we develop an efficient computational method for approximating the Nash solution for the corresponding Nash bargaining game.