The general graph matching game: Approximate core

The classic paper of Shapley and Shubik (1971) characterized the core assignment game using ideas from matching theory LP-duality their highly non-trivial interplay. Whereas this is always non-empty, that general graph can be empty. This salvages situation by giving an imputation in 2/3-approximate for latter; moreover computed polynomial time. bound best possible, since it integrality gap natural underlying LP. Our profit allocation method goes further: multiplier on agent often better than 23 lies interval [23,1], depending how severely constrained is.