Noname manuscript No. (will be inserted by the editor) On the Core and Nucleolus of Directed Acyclic Graph Games Bal´ azs Sziklai · Tam´ as Fleiner · Tam´ as Solymosi Received: date / Accepted: date Abstract We introduce directed acyclic graph (DAG) games, a generalization of standard tree games, to study cost sharing on networks. This structure has not been previously analyzed from a cooperative game theoretic perspective. Every monotonic and subadditive cost game – including monotonic minimum cost spanning tree games – can be modeled as a DAG-game. We provide an ef- ficiently verifiable condition satisfied by a large class of directed acyclic graphs that is sufficient for the balancedness of the associated DAG-game. We intro- duce a network canonization process and prove various structural results for the core of canonized DAG-games. In particular, we characterize classes of coalitions that have a constant payoff in the core. In addition, we identify a subset of the coalitions that is sufficient to determine the core. This result also guarantees that the nucleolus can be found in polynomial time for a large class of DAG-games. Keywords Cooperative game theory · Core · Nucleolus · Directed acyclic graphs · Dually essential coalitions B. Sziklai Momentum Game Theory Research Group, Centre for Economic and Regional Studies, Hun- garian Academy of Sciences and Corvinus University of Budapest, Department of Operations Research and Actuarial Sciences E-mail: sziklai.balazs@krtk.mta.hu T. Fleiner Budapest University of Technology and Economics, Department of Computer Science and Information Theory E-mail: fleiner@cs.bme.hu T. Solymosi Corvinus University of Budapest, Department of Operations Research and Actuarial Sci- ences, and MTA-BCE Momentum Research Group on Strategic Interactions E-mail: tamas.solymosi@uni-corvinus.hu