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