Resource Allocation with Warranties in Claims Problems

The establishing of warranties in order to ensure some minimum awards to each agent involved in an allocation (claims) problem has been analyzed in the body of literature by introducing lower bounds. When focusing on claims problems, four main lower bounds on awards have been defined: the minimal right (Curiel et al., 1987), the fair lower bound (Moulin, 2002), securement (Moreno-Ternero and Villar, 2004) and the min lower bound (Dominguez, 2013). The current approach analyzes the effect of requiring the aforementioned lower bounds in an allocation mechanism. We compare the mechanisms thus obtained together with the use of some additional properties. By doing so, we show that there is a correspondence between lower bounds and claims rules, i.e., associated to each particular lower bound, we find a particular claims rule. Consequently, we provide new characterizations for the constrained equal awards rule, as well as the Ibn Ezra proposal. Finally, a dual analysis, by using upper bounds in awards, provides characterizations of the dual rules of the previous ones: the constrained equal losses rule and the dual of the Ibn Ezra rule.