Non-manipulability by clones in bankruptcy problems
Calleja, P. and LLerena, F. (2022): "Non-manipulability by clones in bankruptcy problems", Economics Letters
Bankruptcy problems (O'Neill, 1982) deal with situations where an amount of a perfectly divisible resource should be distributed among a group of agents presenting conflicting claims, that is, the total amount to divide is not enough to fulfill all demands. These problems are solved by rules proposing an allocation vector that takes into consideration the specifics of the agents.
An important topic in economics is the study of rules that are immune to the strategic behavior of the agents by misrepresenting their characteristics. For the bankruptcy problem, O'Neill (1982) introduces non-manipulability (or strategy-proofness) as the combination of non-manipulability via merging and splitting.
The proportional rule makes agents' payments proportional to their demands and it is one of the most commonly used proposals in real-life situations when a firm goes into bankruptcy. Due to its central role in both practice and theory, it has been extensively analyzed from an axiomatic viewpoint. Here, we limit our attention to splits and mergers involving identical agents, that is, with the same claim. It is quite usual in a real economy for agents (firms) with some common attributes to create a joint venture or for an agent to split into similar new spin-offs, although these practices involving very different agents are reproved. A natural and simple way to formally accommodate these ideas is to restrict the possibility of manipulating to symmetric agents or clones. We name this axiom non-manipulability by clones. Interestingly, we show that this substantially weaker form of non-manipulability is enough to uniquely determine the proportional rule for the realistic case in which all claims are zero o rational numbers. We extend this result to the general domain of bankruptcy problems by adding either claim monotonicity or claims continuity. While claims continuity enforces that small changes in the claims of the agents do not lead to large changes in the awards recommendation, claim monotonicity requires that if only one agent's claim increases, she should not be worse-off.