Allocation problem with random right to accept offers

Abstract

In the paper, we analyze a modifi cation of the allocation problem. The problem can be formulated as follows: sellers in trading agency have a right to sell goods at price offered by the buyer. To this aim, they observe offers which appear at jump times of a Poisson process which are at the same time the decision moments. A reward of the seller who accepted the offer is equal to the discounted value of the selected offer. The right to accept or reject the presented offer is given only to one of the sellers at the moment of appearance of the offer. Once rejected, offer cannot be considered again nor can it be considered by other sellers. The right to make the decision concerning the acceptance or rejection of a presented offer is assigned in random way, such that the probability of obtaining this right by each of the sellers is equal. The aim is to fi nd the strategy which allows to maximize the sum of expected rewards of the sellers under the condition that each of them should earn the same amount of money on average.