Core allocations in Co-investment problems

Abstract

In a co-investment problem a set of agents face a surplus-sharing situation with a single input and a single output exhibiting increasing average returns. All agents contribute their respective inputs and expect part of the collective output. Focusing on the core of the problem, we analyze whether a core allocation of the output is acceptable or compatible with a variation on input contributions, where larger payoffs are expected by those agents whose contribution is increased. We state a necessary and sufficient condition for a core allocation to be acceptable. We also introduce and study the acceptable core, that is, those core allocations acceptable with respect to any possible increase of inputs. Finally we axiomatically characterize when a set-solution that contains acceptable core allocations shrinks into the proportional allocation.