# Stochastic Game Analysis of Cooperation and Selfishness in a Random Access Mechanism
## 7 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Cooperative User**} & \multicolumn{4}{c}{**Non-Cooperative User**} \\ \(p_{a}\) & \(P_{col}\) & \(q_{c}^{*}\) & \(TH_{c}^{i}\) & \(D_{c}\) & \(S_{c}\) & \(q_{nc}^{*}\) & \(TH_{nc}^{i}\) & \(D_{nc}\) & \(S_{nc}\) \\ \hline
0.0001 & \(2.53\times 10^{-10}\) & \(4.14\times 10^{-1}\) & \(1.00\times 10^{-4}\) & 1.00 & \(1.50\times 10^{-9}\) & 0.8787 & \(1.00\times 10^{-4}\) & 1.00 & \(1.55\times 10^{-10}\) \\
0.1 & \(2.14\times 10^{-1}\) & \(1.61\times 10^{-1}\) & \(5.29\times 10^{-2}\) & 7.38 & 3.38 & 0.9999 & \(7.21\times 10^{-2}\) & 2.37 & \(1.98\times 10^{-1}\) \\
0.2 & \(2.64\times 10^{-1}\) & \(8.08\times 10^{-2}\) & \(4.21\times 10^{-2}\) & 18.28 & 7.29 & 0.9999 & \(1.30\times 10^{-1}\) & 2.21 & \(3.17\times 10^{-1}\) \\
0.3 & \(3.05\times 10^{-1}\) & \(7.07\times 10^{-2}\) & \(3.26\times 10^{-2}\) & 27.24 & 8.57 & 0.9999 & \(1.70\times 10^{-1}\) & 2.21 & \(4.36\times 10^{-1}\) \\
0.4 & \(3.11\times 10^{-1}\) & \(6.06\times 10^{-2}\) & \(2.52\times 10^{-2}\) & 37.30 & 9.15 & 0.9999 & \(2.20\times 10^{-1}\) & 2.10 & \(4.95\times 10^{-1}\) \\
0.5 & \(3.47\times 10^{-1}\) & \(6.06\times 10^{-2}\) & \(1.88\times 10^{-2}\) & 51.19 & 9.48 & 0.9999 & \(2.50\times 10^{-1}\) & 2.15 & \(5.93\times 10^{-1}\) \\
0.6 & \(3.25\times 10^{-1}\) & \(5.05\times 10^{-2}\) & \(1.37\times 10^{-2}\) & 71.58 & 9.67 & 0.9999 & \(3.00\times 10^{-1}\) & 1.97 & \(5.88\times 10^{-1}\) \\
0.7 & \(2.92\times 10^{-1}\) & \(4.04\times 10^{-2}\) & \(9.02\times 10^{-3}\) & 109.65 & 9.81 & 0.9999 & \(3.40\times 10^{-1}\) & 1.79 & \(5.50\times 10^{-1}\) \\
0.8 & \(2.44\times 10^{-1}\) & \(3.03\times 10^{-2}\) & \(4.85\times 10^{-3}\) & 205.01 & 9.90 & 0.9999 & \(3.90\times 10^{-1}\) & 1.60 & \(4.76\times 10^{-1}\) \\
0.9 & \(9.99\times 10^{-4}\) & \(1.00\times 10^{-4}\) & \(1.14\times 10^{-5}\) & \(8.70\times 10^{4}\) & 9.99 & 0.9999 & \(4.97\times 10^{-1}\) & 1.00 & \(1.99\times 10^{-3}\) \\
0.9999 & \(9.99\times 10^{-4}\) & \(1.00\times 10^{-4}\) & \(9.99\times 10^{-9}\) & \(1.00\times 10^{8}\) & 10.00 & 0.9999 & \(4.99\times 10^{-1}\) & 1.00 & \(1.99\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance evaluation in the case of \(M=10\) and \(N=2\). \(P_{col}\) is the system collision probability, \(TH_{c}^{i}\) and \(TH_{nc}^{j}\) are the individual throughputs of a cooperative user \(i\) and a selfish user \(j\), respectively. * [PERSON] et al. (2018) [PERSON]; [PERSON] [PERSON]; [PERSON] A stochastic game analysis of the slotted ALOHA mechanism combined with zigzag decoding and transmission cost. In _International Conference on Innovations in Bio-Inspired Computing and Applications_; Springer International Publishing: Cham, Swiztherland, 2018; Volume 735, pp. 102-112. * _[PERSON] et al. (2018)_ [PERSON]; [PERSON]; [PERSON] [PERSON] ZigZag decodable coded slotted ALOHA. In Proceedings of the 2018 15 th Workshop on Positioning, Navigation and Communications (WPNC), Bremen, Germany, 25-26 October 2018; pp. 1-6. * _[PERSON] (2000)_ [PERSON] Performance analysis of the IEEE 802.11 distributed coordination function. _IEEE J. Sel. Areas Commun._**2000**, _18_, 535-547. [CrossRef]
* _[PERSON] et al. (2021)_ [PERSON]; [PERSON]; [PERSON] [PERSON] MiSTA: Threshold-ALOHA with Mini Slots. In Proceedings of the 2021 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), Bucharest, Romania, 24-28 May 2021; pp. 1-6. * _[PERSON] et al. (2019)_ [PERSON]; [PERSON] Design and performance evaluation of successive interference cancellation-based pure ALOHA for Internet-of-Things networks. _IEEE Internet Things J._**2019**, \(6\), 6578-6592. [CrossRef]
* _[PERSON] et al. (2017)_ [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] Mathematical model of LoRaWAN channel access with capture effect. In Proceedings of the 2017 IEEE 28 th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Montreal, QC, Canada, 8-13 October 2017; pp. 1-5. * _[PERSON] et al.