Resource allocations with guaranteed awards in claims problems

Abstract The notion of lower bound on awards has been introduced in the literature to analyze establishment guarantees that ensure a minimum award each agent involved situations conflicting claims, such as rationing resource or distribution assets bankrupt firm. Indeed, this concept core role many approaches related problem fair allocation (Thomson Math Soc Sci 74:41–59, 2015) and range bounds have proposed: minimal right (Curiel et al. Z Oper Res 31:A143–A159, 1987), (Moulin Handb Choice Welf 1:289–357, 2002), securement (Moreno-Ternero Villar 47(2):245–257, 2004) $$\min $$ min (Dominguez mimeo, 2006). In context, key contribution current paper is show there correspondence between rules; i.e., associated particular bound, we find specific way distributing resources. doing so, provide new characterizations for two well known rules, constrained equal Ibn Ezra’s rules. A dual analysis, by using upper will previously mentioned rules: losses rule rule.