This paper focuses on cooperative games with transferable utility. We propose the computation of two solutions, the Shapley value for n agents and the nucleolus with a maximum of four agents. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud and the random arrival rules.

Despite global environmental governance has traditionally couched global warming in terms of annual CO 2 emissions (a flow), global mean temperature is actually determined by cumulative CO 2 emissions in the atmosphere (a stock). Thanks to advances of scientific community, nowadays it is possible to quantify the "global carbon budget", that is, the amount of available cumulative CO 2 emissions before crossing the 2 o C threshold (Meinshausen et al., 2009). The current approach proposes to analyze the allocation of such global carbon budget among countries as a classical conflicting claims problem (O'Neill, 1982). Based on some appealing principles, it is proposed an efficient and sustainable allocation of the available carbon budget from 2000 to 2050 taking into account different environmental risk scenarios.

This paper proposes to use claims models as a reasonable and operative alternative in order to allocate CO 2 emissions by countries (or groups), in the framework of multilateral negotiations and the fight against climate change. This framework has two characteristics which fits this type of claims models: a restrictive global endowment (the maximum world emissions permitted) and the excess of emissions (and demand) by countries. The proposed methodology consists on establishing some requirements that any admissible distribution solution should satisfy, examining a broad group of theoretical distribution solutions emerged from the specific literature and analyzing their application according to reasonable ordering criteria linked to equity and stability properties. The proposed theoretical framework is applied empirically to an analysis by groups of countries in the period 2010-2050, using various world endowments from Meinshausen et al. (2009), together with claims forecasts associated with the RCP scenarios. The results obtained point out that for intermediate claims scenarios the solutions associated with the constrained equal awards (CEA) and α-minimal (α-min) solutions are typically selected. In particular, these two solutions are clearly equity-sensitive, where the efforts to be made by Asia and OECD are very important, as a whole, and especially in the case of the CEA. Given these circumstances, and the better balance between equity and proportionality associated to the α-min allocation methodology maybe that one would be more operative and acceptable.

In this paper, we characterize the non-emptiness of the equity core (Selten, 1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta-Ray, 1991). Both results are based on a geometrical decomposition of the equity core as a finite union of polyhedrons.

The financial and economic crisis in Spain during recent years has induced public budget adjustments. The crisis has caused a great social impact due to the way the austerity measures have been implemented, affecting mainly key economic sectors such as the civil service, justice, education and health. Among all of these sectors, the current paper focuses on the health budget distribution, since the changes in the provision of the health services induce faster and clearer impacts in the social welfare. Spain is divided into 17 regions, and each region manages its own health system. Specifically, we analyze the Catalan health budget assignment since Catalonia is one of the most populated regions and one where the restrictions have been more evident. We study the health budget distribution for the period 1998-2014, from the point of view of the conflicting claims problem (O'Neill, 1982). Accordingly, alternative allocations of the health budget are proposed by using some of the most used solutions in the body of literature. Finally, in order to choose the most appropriate solution, we require the fulfillment of (i) some equity and stability criteria, and (ii) some commonly accepted social constraints.