4.2.6. Experiment Six

Aim: The last set of experiments was implemented to compare the suggested recovery model (the extended version with three players) with our previous version (modelling by two players). The precision (accuracy) rate has been used for assessment according to the recovery probabilities for multi degrees of handoff threshold values that are considered as a very influential factor to complete the retrieval process.

Main Results: As expected, Form Figure 9, utilizing three players for game modelling, increases the precision rate by an average of 5% compared with two players for a game.

Discussion: This improvement comes from increasing competition through utilizing more than two recovery algorithms that gave the opportunity to select the best protocol from a pool of algorithms according to the current MDS environmental conditions. Therefore, some protocols used in our previous work [21] will be retreated in this work due to the entry of other protocols in the competition.

**Figure 8.** A loss packet analysis with a comparative model.

**Figure 9.** Accuracy analysis between two-player- and three-player-based game modeling.

#### **5. Conclusions and Future Work**

The purpose of this paper was to propose a new game theory model for determining the optimal recovery strategy in MSD. The novel method was compared against three of the most commonly used MDS recovery procedures in a competitive environment. Game theory is founded on the idea that each algorithm chooses the most appropriate strategy in terms of message delivery time and message count in order to determine the right recovery solution based on environmental factors. A key step of a quantum game-theoretic research is identifying which strategy to a recovery process is the superior solution to the strategies chosen by others. The proposed recovery model is based on the development of a knowledge base that is used to choose the best appropriate method based on the reward matrix and dominant equilibrium technique. The experimental findings demonstrate the superiority of the suggested recovery paradigm. In the future, it may be essential to include more recovery procedures to optimize the suggested model's performance. Additionally, a hybrid method based on game theory and the recently developed paradigm of cloud algorithms was utilized to improve the outcome. Furthermore, this enhanced the game model to allow interactions between players and utilized mixed strategies. Prior to that, some investigations should be made into the probability distribution of the behavior of the competing players (dealing with uncertainty). The application of the proposed model in the case of large systems and the discussion of its complexity will be also done in future work. Finally, the concept of mind-light-matter unity AI/QI in quantum-inspired computing can be utilized to enhance the suggested model.

**Author Contributions:** Conceptualization, M.M.M., S.M.D. and Y.F.M.; methodology, S.M.D. and Y.F.M.; software, Y.F.M.; validation, M.M.M. and S.M.D.; formal analysis, M.M.M., S.M.D. and Y.F.M.; investigation, M.M.M. and S.M.D.; resources, S.M.D. and Y.F.M.; data curation, S.M.D. and Y.F.M.; writing—original draft preparation, M.M.M., S.M.D. and Y.F.M.; writing—review and editing, M.M.M. and S.M.D.; visualization, Y.F.M.; supervision, M.M.M. and S.M.D.; project administration, S.M.D. and Y.F.M.; funding acquisition, Y.F.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The study did not report any data.

**Conflicts of Interest:** The authors declare no conflict of interest.
