Compromising in bifocal distribution games: the average value

It is well known that, in distributions problems, fairness rarely leads to a single viewpoint (see, for instance, Young, Equity in theory and practice. Princeton University Press, Princeton, 1994). In this context, this paper provides interesting bases that support the simple and commonly observed behavior of reaching intermediate agreements when two prominent distribution proposals highlight a discrepancy in sharing resources. Specifically, we formalize such a conflicting situation by associating it with a ‘natural’ cooperative game, called bifocal distribution game, to show that both the Nucleolus (Schmeidler, SIAM J Appl Math 17:1163–1170, 1969) and the Shapley value (Shapley, Additive and non‐additive set functions. Princeton University, Princeton, 1953a) agree on recommending the average of the two focal proposals. Furthermore, we analyze the interpretation of the previous result by means of axiomatic arguments.