At this point, we would like to give an overview of possible future directions of research and ideas that could be pursued to expand the work of this thesis.
To obtain a more precise idea of the influence of characteristics on the computational complexity of solution concepts applied to shortest path games, we think that it would be particularly interesting to analyse various stability concepts for different non-simple variants of shortest path games. Especially, the core, least-core and nucleolus would be important stability concepts to analyse in this context. We also think that it would be interesting to prove several open problems for those graph-based games, which we presented in this thesis, and to look for further graph-based coalitional games to extend the sample space of graph-based games. So, having a more complete set of results we might be able to isolate influential properties and characteristics of graph-based games. This may even allow researchers, interested in transferring problems to graph-based coalitional games, to use it as heuristic to specify coalitional games in such a way that the application of interesting solution concepts is computationally tractable.
We observed during our studies that for many real-world motivated graph-based games, which have been analysed in the literature, the determination of power indices is intractable. For practical appli- cations, where the existence of an efficient algorithm is imperative, this situation is of course unsat- isfactory. But we have also noticed during our research that particular simplifications of graph-based games, most notably simplifications of the underlying graph, can lead to computationally favourable results. For example, the reduction of graphs to trees seemed to be a promising reduction. This is also interesting in a more practical context, because there are many real-world problems with tree- structures in computer science (Internet and networking), which could be analysed from a game- theoretic perspective. Hence, the reduction to trees and also acyclic directed graphs for graph-based games is not only a theoretical consideration to obtain polynomial complexity results, but also a promising way to determine classes of coalitional games, where interesting solution concepts applied to games, which are motivated from real-word problems, are tractable.
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