Competitive Auctions and Envy-Freeness for Group of Agents

In mechanism design, fairness is one of the central criteria for analyzing mechanisms. Recently, a new fairness concept called envy-freeness of a group toward a group (GtG-EFness) has received attention, which requires that no group of agents envies any other group. In this paper, we consider GtG-EFness in more general combinatorial auctions, including several subclasses of the multi-unit auction domain (unit-demand, diminishing marginal values, and all-or-nothing), and reveal the tight bound of the competitive ratios. In particular, we prove that the tight bound of the competitive ratio is 1/k (where k is the number of items) for the general combinatorial auction domain. We also clarify the relationship with Walrasian equilibria and conclude that no group envies any other group in any Walrasian equilibrium.

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