It is well known that, in distributions problems, "Fairness" rarely leads to a single viewpoint (see Young (1994) and Moulin (1988) among many others). This paper provides, in this context, interesting basis in defense of intermediate agreements when two prominent proposals, representing different sets of "Equity Principles", highlight a discrepancy in sharing resources. Specifically, we formalize such a conflicting situation by associating it with a "natural" cooperative game, called the Bifocal Distribution game, to show that both the Nucleolus, introduced by Schmeidler (1969), and the Shapley value, proposed by Shapley (1953), agree on recommending the "average of the two focal solutions". Finally, applying our analysis to bankruptcy problems, which have been analyzed extensively by Thomson (2003) and Moulin (2002), provides new "reasonable" solutions.distribution problems, bankruptcy, cooperative games, nucleolus, Shapley value, Lorenz criterion.
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