**Wednesday, 16:15 - 16:40 h, Room: MA 043**

**Kazutoshi Ando**

Computation of the Shapley value of minimum cost spanning tree games: #P-hardness and polynomial cases

**Abstract:**

We show that computing the Shapley value of minimum cost spanning tree games is #P-hard even if the cost functions of underlying networks are restricted to be *{0,1}*-valued. The proof is by a reduction from counting the number of minimum 2-terminal vertex cuts of an undirected graph, which is #P-complete. We also investigate minimum cost spanning tree games whose Shapley values can be computed in polynomial time. We show that if the cost function of the given network is a subtree distance, which is a generalization of a tree metric, then the Shapley value of the associated minimum cost spanning tree game can be computed in O*(n*^{4}) time, where *n* is the number of players.

Talk 3 of the contributed session Wed.3.MA 043

**"Solving cooperative games"** [...]

Cluster 8

**"Game theory"** [...]