# Utility Distribution Strategy of the Task Agents in Coalition Skill Games
## 5 Simulation Results
Because TAAUDA is polynomial, it is acceptable for the most practical applications. Simulation 3: In this simulation, 15 groups of data sets numbered 3.1 to 3.15 (named data set 3) were generated by the following methods: The size of which were \(n=30\), \(l=15\), and \(m=30\). Each service agent in group \(d\in\{1,2,\cdots,15\}\) possesses \(d\) skills, which skill is possessed is random. Each task agent in group \(d\in\{1,2,\cdots,15\}\) needs \(d\) skills, which skill is needed is random. For \(t_{k}\in T\), \(u_{k}\gets TSN_{k}\times random(1,m/2)\). The average system revenues of TAAUDA, the General Genetic Algorithm, Vig and Adams Algorithm, and Service and Adams Algorithm are shown in Table 7. Figure 6 displays the average system revenues of TAAUDA, the Combinatorial Bids based Algorithm, and Computationally Efficient Sampled Fictitious Play. The average run time of the 6 algorithms is shown in Figure 7. The parameters of TAAUDA in Simulation 3 were set as: \(DRS=4\), \(DN=7\), and \(IN=10^{5}\). It can be seen from the results in Table 7, Figure 6, and Figure 7, that in most cases, the average system revenues obtained by TAAUDA are better than those of the other 5 algorithms and the run time of TAAUDA is shorter than that of the General Genetic Algorithm, which is similar to the results of Simulation 2. The effectiveness of TAAUDA is further verified. Simulation 4: In this simulation, 12 groups of data sets numbered 4.1 to 4.12 (named data set 4) were generated based on iMOPSE, which was created based on the real-life project instances received from international enterprise (Volvo IT): Data 4.1-4.4 were extracted from data set 200-40-133-15, 4.5-4.8 were extracted from data set 200-40-45-15, and 4.9-4.12 were extracted from data set 200-40-91-15. Resources in iMOPSE can be seen as service agents, a total of 30 service agents and a total of 30 tasks were extracted randomly from the corresponding data sets. Some modifications were made on the extracted data: the salaries of resources and the durations of the tasks were ignored. A total of _random_(1,11) skills were added to each task, this is because each task in iMOPSE needs only one skill, which is inconsistent with the case of this paper. For \(t_{k}\in\) T, \(u_{k}\gets TSN_{k}\times random(1,m/2)\). The average system revenues of TAAUDA, the General Genetic Algorithm, Vig and Adams Algorithm and Service, and Adams Algorithm are shown in Table 8. Figure 8 displays the average system revenues of TAAUDA, the Combinatorial Bids based Algorithm, and Computationally Efficient Sampled Fictitious Play. The average run time of the 6 algorithms is shown in Figure 9. The parameters of TAAUDA in Simulation 4 were set as: \(DRS\) = 4, \(DN\) = 7, and \(IN\) = 10\({}^{5}\). It can be seen from the results of Table 8 and Figures 8 and 9 that in most cases, the average system revenues obtained by TAAUDA are better than those of the other 5 algorithms and that the run time of TAAUDA is shorter than that of the General Genetic Algorithm. The effectiveness of TAAUDA is further verified. Simulation 5: This simulation checks the influences of the utility distribution scheme on the system revenue. The comparison algorithm assumes that each task agent always distributes its utility equally to the needed skills. Other settings are exactly the same as TAAUDA. The comparison algorithm is called the task allocation through distributing utilities averagely (TADUA). With different data, we ran TAAUDA and TADUA 100 times, the average system revenues are shown in Tables 9-12 (Table 9 for data set 1, Table 10 for data set 2, Table 11 for data set 3, and Table 12 for data set 4). The parameters of TAAUDA and TADUA were both set as: \(DRS=3\), \(DN=6\), and \(IN=10^{5}\). It can be concluded from the simulation results, that in most cases, adjusting the utility distribution schemes of