Group Strategyproof Cost Sharing: The Role of Indifferences

Every agent reports his willingness to pay for one unit of good. A mechanism allocates goods and cost shares to some agents. We characterize the group strategyproof (GSP) mechanisms under two alternative continuity conditions interpreted as tie-breaking rules. With the maximalist rule (MAX) an indierent agent is always served. With the minimalist rule (MIN) an indierent agent does not get a unit of good. GSP and MAX characterize the cross-monotonic mechanisms. These mechanisms are appropriate whenever symmetry is required. On the other hand, GSP andMIN characterize the sequential mechanisms. These mechanisms are appropriate whenever there is scarcity of the good. Our results are independent of an underlying cost function; they unify and strengthen earlier results for particular classes of cost functions.