According to section 2.2.1, using Shapely’s value method, profit sharing was done among members of the diagnostic laboratory network. Table 5 shows the results of profit sharing in a numerical example. In Table 5, the profit of each laboratory is equal to the weighted average of the Shapely’s values of laboratories (Table 4). In Table 5, the profit sharing is represented by both percentages and earnings. We assume that if the income of this diagnostic network is ten billion Rials throughout the next year, then it would be possible to predict the profits of laboratories using the percentage of each laboratory’s profit.
The profit sharing results show that the better the performance of the labs, the greater the level of satisfaction of patients, because the accuracy of the test results is an effective factor in the selection of laboratories by patients. In this case, by increasing the level of performance of laboratories, the number of samples of these centers has increased, which has a direct impact on the amount of network income. Therefore, the collaboration between the laboratories will increase their efficiency by sharing resources, thus increasing the quality of the results of the tests of these centers, the number of patients and, eventually, the sample size of these centers. Table 3 shows the increasing utility of coalitions with the arrival of a laboratory in each coalition.
In collaborative networks of various actors, a mechanism based on equality is often used to profit profit sharing in the network. In cooperative games, Shapley’s value has the nature of fair profit sharing. Since the network of medical diagnostics laboratories, through promotion of cooperation among members, has the properties of a cooperation network, the Shapely approach helps to predict the fair profit sharing among network members. The results show that for such a fair mechanism, the efficiency and sample size, as the two effective factors, have a decisive role in the share of profit of laboratory units of the network because in the laboratory services network, members receive a number of samples according to their performance, which has a direct impact on net income. In this case, trying to make more money by network members should be in such a way as to meet the needs of the network for its lifecycle. Hence, to set up and maintain a diagnostic network, managers are advised to consider the following: (1) Selected criteria for profit sharing must be quantitative in nature in order to be measurable. Therefore, the number of samples and the efficiency, as two effective factors, can have an effective role in the profit sharing of network members. (2) Given the lifecycle of the network of the diagnosis laboratories and the requirements for the network formation stage, the resources used to share profits should be the requirements for the establishment of a shared network of diagnostic laboratories. Therefore, performance evaluation in identifying requirements for network infrastructure will help to create appropriate infrastructure for demand and ultimately increase sample size. (3) Since profit sharing has a strategic property, profit sharing in the network life cycle should create competitive advantage and provide an incentive for attracting and investing members from a strategic perspective, which is also effective in improving member performance and ultimately in accepting more sample numbers.