# Improving Computational Efficiency in Crowded Task Allocation Games with Coupled Constraints
## 6 Conclusions  
In this paper, we introduced a game-theoretic framework for allocation of tasks with spatial and temporal coupled constraints first seen in CCBBA. A game-theoretic modeling of such problems helps to overcome potential convergence issues faced in a market-based allocation model through leveraging on the properties of potential games. A well-designed game model alone can effectively overcome spatial relationships among tasks and when coupled with the scheduling algorithm, allows feasible assignment of tasks with both spatial and temporal dependencies. Additionally, existing equilibrium selection algorithms have commonly been restricted by the size of the problem, making implementation of game-theoretic theoretic task allocation impractical for large-scale problems. However, by using random sampling in DSA, it is possible to obtain a feasibly good solution within a short time, allowing game-theoretic implementations in emergency operations which frequently consist of large numbers of tasks with complex relationships and yet require quick allocation at the same time.  
The greatest limitation for the proposed methodology lies in the inability to quantify or guarantee the optimality of any given solution, in terms of global allocation, despite its feasibility to provide an allocation solution that considers the spatial and temporal relationships between the different types of task. A plausible explanation may be due to the existence of multiple Nash equilibria and the probabilistic approach in DSA. Additional studies to limit the game model to have only a single Nash equilibrium or to consider deterministic equilibrium selection algorithms that are a capable of selecting the Nash equilibrium with the maximum global allocation scores will help to overcome this deficiency.  
Despite the current flaws in the proposed methodology, reasonably good solutions can still be obtained quickly to tackle coupled-constraint task allocation problem in a crowded space.  
Figure 9: Mean computation times for various sample sizes.  
**Author Contributions:** Conceptualization, M.C.L. and H.-L.C.; methodology, M.C.L.; software, M.C.L.; validation, M.C.L. and H.-L.C.; formal analysis, M.C.L.; investigation, M.C.L.; resources, H.-L.C.; data curation, M.C.L.; writing--original draft preparation, M.C.L.; writing--review and editing, M.C.L. and H.-L.C.; visualization, M.C.L.; supervision, H.-L.C.; project administration, H.-L.C.; funding acquisition, H.-L.C.  
**Funding:** This work was supported in part by Information Communication Technology Research and Development program of Institute for Information & Communications Technology Planning and Evaluation (IITP) grant funded by the Korea government Ministry of Science and ICT (NO.R1711055271, Development of High Reliable Communications and Security Software for Various Unmanned Vehicles).  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
**Abbreviations**  
The following abbreviations are used in this manuscript:  
CCBBA Coupled-Constraint Consensus-Based Bundle Algorithm  
CBBA Consensus-Based Bundle Algorithm  
DSA Distributed Stochastic Algorithm