Convergence under Replication of Rules to Adjudicate Conflicting Claims

We study the behavior of rules for the adjudication of con°icting claims when there are a large number of claimants with small claims. We model such situations by replicating some basic problem. We show that under replication, the random arrival rule (O'Neill, 1982) behaves like the proportional rule, the rule that is the most often recommended in this context. Also, under replication, the minimal overlap rule (O'Neill, 1982) behaves like the constrained equal losses rule, the rule that selects a division at which all claimants experience equal losses subject to no-one receiving a negative amount.Claims problems, Replication, Random arrival rule, Proportional rule, Minimal overlap rule, Constrained equal losses rule.

Consistency and the sequential equal contributions rule for airport problems

We consider the problem of sharing the cost of a public facility among agents who have different needs for it. We base two characterizations of the sequential equal contributions rule on smallest-cost consistency. Namely, (i) the rule is the only rule satisfying equal treatment of equals, independence of all but the smallest-cost, and smallest-cost consistency, and (ii) it is the only rule satisfying equal share lower bound, cost monotonicity, and smallest-cost consistency.mathematical economics;

A characterization of the Vickrey rule in slot allocation problems

We study the slot allocation problem where agents have quasi-linear single-peaked preferences over slots and identify the rules satisfying efficiency, strategy-proofness, and individual rationality. Since the quasi-linear single-peaked domain is not connected, the famous characterization of the Vickrey rule in terms of Holmström (1979)'s three properties cannot be applied. However, we are able to establish that on the quasi-linear single-peaked domain, the Vickrey rule is still the only rule satisfying efficiency, strategy-proofness, and individual rationality

On the Coincidence of the Shapley Value and the Nucleolus in Queueing Problems

Given a group of agents to be served in a facility, the queueing problem is concerned with finding the order to serve agents and the (positive or negative) monetary compensations they should receive. As shown in Maniquet (2003), the minimal transfer rule coincides with the Shapley value of the game obtained by defining the worth of each coalition to be the minimum total waiting cost incurred by its members under the assumption that they are served before the non-coalitional members. Here, we show that it coincides with the nucleolus of the same game. Thereby, we establish the coincidence of the Shapley value and the nucleolus for queueing problems. We also investigate the relations between the minimal transfer rule and other rules discussed in the literature

The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources

We consider a problem where a group of agents is interested in some goods provided by a supplier with multiple sources. To be served, each agent should be connected directly or indirectly to all sources of the supplier for a safety reason. This problem generalizes the classical minimum cost spanning problem with one source by allowing the possibility of multiple sources. In this paper, we extend the definitions of the folk rule to be suitable for minimal cost spanning tree problems with multiple sources and present its axiomatic characterizations

The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources

We consider a problem where a group of agents is interested in some goods provided by a supplier with multiple sources. To be served, each agent should be connected directly or indirectly to all sources of the supplier for a safety reason. This problem generalizes the classical minimum cost spanning problem with one source by allowing the possibility of multiple sources. In this paper, we extend the definitions of the folk rule to be suitable for minimal cost spanning tree problems with multiple sources and present its axiomatic characterizations