Loss calibrated rationing methods

The standard problem of rationing a single overdemanded commodity ([11], [2], [16]) has a natural bipartite extension with multiple types of a one-dimensional commodity (e.g., jobs with di erent skill requirements), and each agent can only consume some types of the resource (e.g., workers have di erent skills). We de ne the new standard loss calibrated rationing methods, that equalize across agents the ratio of shares to (calibrated) losses (demand minus share). We extend them to bipartite methods that 1) are not affected by the elimination of an edge and the corresponding ow (Consistency), and 2) treat resource types with identical connectivity as a single type. They are essentially the only standard methods with a bipartite extension meeting the two properties above. Most of the parametric methods discussed in the literature ([16], [17]) do not admit such extension.

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