A multi-unit assignment valuation is a function represented by a weighted bipartite graph. In this paper, we provide a characterization of such a function in terms of maximizer sets of perturbed functions. We then present an algorithm that checks whether a given bivariate function is a multi-unit assignment valuation, and if the answer is “yes,” computes a weighted bipartite graph representing the function.
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Otsuka et al. (2023) studied this question.
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