In a theoretical 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 of input contributions, where larger payoffs are expected by those agents whose contribution has 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 for any possible increase of inputs. Finally, we axiomatically characterize when a set-solution that contains acceptable core allocations shrinks into the proportional allocation.

在理论上的共同投资问题中，一组代理人面临盈余共享的情况，即单一投入和单一产出表现出不断增加的平均回报。所有代理商都贡献各自的投入，并期望集体产出的一部分。着眼于问题的核心，我们分析了产出的核心分配是可接受的还是与投入贡献的变化兼容的，投入增加的代理商期望得到更大的回报。我们声明核心分配被接受的必要和充分条件。我们还将介绍和研究可接受的核心，即，对于任何可能的投入增加而言可接受的核心分配。最后，我们根据公理来表征何时包含可接受的核心分配的集合解决方案缩小为比例分配。