# Utility Distribution Strategy of the Task Agents in Coalition Skill Games
## 5 Simulation Results
In Simulation 1, 15 groups of data sets numbered 1.1 to 1.15 (named data set 1) and 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 all the 15 groups of data sets needs _random_(1,5) skills, which skill is needed is random. For \(t_{k}\)\(\in\)\(T\), \(u_{k}\)\(\leftarrow\)\(TSN_{k}\)\(\times\)_random_(1,\(m/2\)). The average system revenues of TAAUDA, the General Genetic Algorithm, Vig and Adams Algorithm, and Service and Adams Algorithm (the agents in the latter three algorithms are not self-interested) are shown in Table 5. Figure 2 displays the average system revenues of TAAUDA, the Combinatorial Bids based Algorithm, and Computationally Efficient Sampled Fictitious Play, the agents in which are all self-interested. The average run time of the 6 algorithms is shown in Figure 3. In simulations 1-5, all the algorithms ran 100 times, and the average system revenues and average run time were computed. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & 0.01 & 0.05 & 0.1 & 0.15 & 0.2 & 0.3 & 0.4 & 0.6 & 0.8 & 0.9 & 0.95 \\ \hline
0.01 & 415.1 & 440.0 & 441.8 & 474.3 & 508.3 & 515.8 & 543.8 & 552.3 & 566.0 & 584.0 & 581.3 \\
0.05 & 483.3 & 506.5 & 524.0 & 563.5 & 558.5 & 568.8 & 595  
From the results in Table 5 and Figure 2, show that in most cases the average system revenues obtained by TAAUDA are better than those of other 5 algorithms. It can also be concluded from Figure 3 that the run time of TAAUDA is shorter than that of the General Genetic Algorithm and Vig and Adams Algorithm. Figure 3: The average runtime of the 6 algorithms. Figure 2: The average system revenues of TAAUDA, CBA, and CESFP. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & TAAUDA & GGA & VAA & SAA \\ \hline
1.1 & 220.52 & 157.43 & 230.0 & 206 \\
1.2 & 344.51 & 291.10 & 322.0 & 322 \\
1.3 & 511.19 & 444.12 & 482.0 & 506 \\
1.4 & 534.55 & 443.08 & 516 & 503 \\
1.5 & 601.67 & 552.42 & 588 & 599 \\
1.6 & 613.37 & 593.28 & 612 & 601 \\
1.7 & 650.32 & 636.84 & 632 & 625 \\
1.8 & 790.2 & 781.14 & 775 & 747 \\
1.9 & 826.86 & 820.5 & 818 & 817 \\
1.10 & 563.54 & 562.92 & 554 & 564 \\
1.11 & 604.36 & 602.12 & 597 & 601 \\
1.12 & 699.0 & 697.72 & 699 & 693 \\
1.13 & 837.85 & 835.32 & 835 & 836 \\
1.14 & 646.0 & 642.86 & 646 & 646 \\
1.15 & 880.0 & 875.86 & 880 & 880 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The average system revenues of TAAUDA, GGA, VAA, and SAA. Simulation 2: In this simulation, 15 groups of data sets numbered 2.1 to 2.15 (named data set 2) were generated by the following methods: The size of which were \(n=30,l=15\), and \(m=30\). Each service agent in all the 15 groups of data sets possesses \(random(1,5)\) 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 \(t\in T\), \(u_{k}\gets TSN_{k}\times random(1,m/2)\). The average system revenues of TAAUDA, the General Genetic Algorithm, Vig and Adams Algorithm, and Service and Adams Algorithm are shown in Table 6. Figure 4 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 5. The parameters of TAAUDA in Simulation 2 were set as: \(DRS=2\), \(DN=3\), and \(IN=10^{5}\). From the results in Table 6 and Figure 4, it can be seen that in most cases the average system revenues obtained by TAAUDA were better than those of the other 5 algorithms. Because each task agent in data set 2.1 needs only one skill, the utility distribution scheme of the task agents will not work, its average system total revenue is smaller than that of the General Genetic Algorithm. It can also be concluded from Figure 5 that the run time of TAAUDA is shorter than that of the General Genetic Algorithm but is longer than that of the rest 4 algorithms.