On Computing the Shapley Value in Queues

The Shapley value solution occupies a central place in fair division literature, specially in settings where a set of positions in a queue need to be shared between a set of agents using payments. But computing the Shapley value of an agent requires solving exponential number of optimization problems (marginal value problem). Moreover, it requires exact knowledge of valuation functions of agents (valuation problem). In this work, we investigate two settings in queues: (i) every agent is interested in at most one position and his value of a position depends on the agents served before him and (ii) every agent may be interested in more than one position and his value for a bundle of positions is independent of the allocations to other agents. We investigate how generalized English auctions for each of these settings can overcome the marginal value problem and valuation problem. While generalized English auction for setting (ii) is already known in the literature, we design a generalized English auction for setting (i).