Benefit’s division with two indivisible components by the procedure allowing negotiations

The article deals with the distribution of partially divisible benefit with two indivisible components between the two beneficiaries at the independent informing each other about their discrete utility functions. The specified information represents the way of division desirable to the beneficiary and the maximum price which they are ready to pay for the implementation of the proposed approach to the benefit’s distribution. The study of the problem is carried out with the assumption of equality of rights and opportunities for beneficiaries which is possible by attracting an arbitrator, independent and indifferent to the participants in the conflict process. The author describes types and conditions of the conflicts’ emergence between the beneficiaries connected with the lack of consensus both on the way of division and on the amount of compensation payment. The article presents the classification of conflicts into one-type groups. The author proposes the optimal ways of division and specially calculated compensation values, not taking into account the factor of envy, understood as the situation when one of the beneficiaries is sure that he/she gets less than the competitor. The cases when it is possible to do without negotiations on the division issue are listed. The author reveals the circumstances when negotiations are possible. Conditions of inevitability of negotiations are pointed out. The cross-disciplinary research is carried out on a joint of mathematics and the social and economic sphere, with the use of their knowledge, provisions, meth ods. The research results can be used in practice in economic activity and political field for smoothing contradictions, typical for human society.