Math Meth Oper Res (2014) 79:353–370 DOI 10.1007/s00186-014-0466-9 ORIGINAL ARTICLE Multi-commodity rationing problems with maxmin payoffs Miguel A. Hinojosa · Amparo M. Mármol Received: 31 March 2013 / Published online: 4 April 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract We address a multi-dimensional extension of standard rationing problems in which several commodities have to be shared among a set of agents who exhibit maxmin preferences on the results they obtain. In this context we investigate efficiency and introduce a property of stability which is supported on a transferable utility game. We also propose a procedure to construct rules for obtaining stable allocations for the special case where all commodities have the same weight. Keywords Rationing problems · Maxmin preferences · Cooperative games 1 Introduction The standard rationing problem consists of the division of a given amount of a per- fectly divisible good among agents who hold claims against it exceeding the avail- able amount. The seminal work on this class of division problems is due to O’Neill (1982). Another important early contribution dealing with this same model is Aumann and Maschler (1985). Since then, the literature has extensively explored the model (see Thomson 2003, 2006 for surveys). In this paper, we address a multi-dimensional extension of standard rationing prob- lems in which the agents exhibit maxmin preferences on the results they obtain with M. A. Hinojosa Departamento de Economía, Métodos Cuantiativos e Historia Económica, Universidad Pablo de Olavide, Ctra. Utrera, Km. 1, 41013 Seville, Spain e-mail: mahinram@upo.es A. M. Mármol (B ) Departamento de Economía Aplicada III, Instituto de Matemáticas (IMUS), Universidad de Sevilla, Seville, Spain e-mail: amarmol@us.es 123