Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations

Exponential runtimes of algorithms for values games with transferable utility like the Shapley value are one biggest obstacles in practical application otherwise axiomatically convincing solution concepts cooperative game theory. We investigate to what extent hierarchical structure a level improves compared an unstructured player set. Representatively, we examine levels value, nested and, as new structures, Owen value. For these values, provide polynomial-time (under normal conditions) which exact and therefore not approximation algorithms. Moreover, introduce relevant coalition functions where all coalitions that payoff calculation have Harsanyi dividend zero. Our results shed light on computation set many from extensions this