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Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single out the most desirable outcomes in terms of appropriate notions of worth distributions, which are usually called solution concepts. Motivated by the fact that decisions taken by realistic players cannot involve unbounded resources, recent computer science literature reconsidered the definition of such concepts by advocating the relevance of assessing the amount of resources needed for their computation in terms of their computational complexity. By following this avenue of research, the paper provides a complete picture of the complexity issues arising with three prominent solution concepts for coalitional games with transferable utility, namely, the core, the kernel, and the bargaining set, whenever the game worth-function is represented in some reasonable compact form (otherwise, if the worths of all coalitions are explicitly listed, the input sizes are so large that complexity problems are---artificially---trivial). The starting investigation point is the setting of graph games, about which various open questions were stated in the literature. The paper gives an answer to these questions, and in addition provides new insights on the setting, by characterizing the computational complexity of the three concepts in some relevant generalizations and specializations.
We study decentralized markets with the presence of middlemen, modeled by a non-cooperative bargaining game in trading networks. Our goal is to investigate how the network structure of the market and the role of middlemen influence the markets effici
We give solutions to two fundamental computational problems in ontology-based data access with the W3C standard ontology language OWL 2 QL: the succinctness problem for first-order rewritings of ontology-mediated queries (OMQs), and the complexity pr
Bargaining networks model the behavior of a set of players that need to reach pairwise agreements for making profits. Nash bargaining solutions are special outcomes of such games that are both stable and balanced. Kleinberg and Tardos proved a sharp
A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the emph{core}--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty
There has been much work on exhibiting mechanisms that implement various bargaining solutions, in particular, the Kalai-Smorodinsky solution cite{moulin1984implementing} and the Nash Bargaining solution. Another well-known and axiomatically well-stud