Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge decomposition and the Shapley value of a cooperative game   We show that a cooperative game may be decomposed into a sum of component
games, one for each player, using the combinatorial Hodge decomposition on a
graph. This decomposition is shown to satisfy certain efficiency, null-player,
symmetry, and linearity properties. Consequently, we obtain a new
characterization of the classical Shapley value as the value of the grand
coalition in each player's component game. We also relate this decomposition to
a least-squares problem involving inessential games (in a similar spirit to
previous work on least-squares and minimum-norm solution concepts) and to the
graph Laplacian. Finally, we generalize this approach to games with weights
and/or constraints on coalition formation.

17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat