Guarantee structures for problems of fair division

We study the problem of fair division in situations where the number of individuals involved may vary while the resources at their disposal remain fixed. We are interested in minimizing the loss that an agent originally present may incur in such circumstances. Given a solution, i.e., a systematic method of solving any division problem in some class, we introduce the notion of its guarantee structure as a measure of the protection it offers to the original agents. We show that the Kalai-Smorodinsky solution offers greater guarantees than any weakly Pareto-optimal and anonymous solution and in particular than the Nash solution.