The concede-and-divide rule for liability problems

Liability problems model the issue of allocating the asset value of an insolvent firm among the creditors and the firm itself. We introduce the concede-and-divide rule for liability problems with at most three agents, i.e. one firm and at most two creditors. Following a game-theoretic approach, we show that all solutions for liability games that satisfy symmetry and translation covariance induce the concede-and-divide rule, in particular the Shapley value and the nucleolus. Moreover, we provide axiomatic characterizations of the concede-and-divide rule using the minimal rights first property. We extend the analysis to liability problems with more agents but an almost solvent firm, i.e. reducing an arbitrary individual liability to zero would make the firm solvent.