We study incentive compatible profit-sharing rules when output (or profit) is obtained via the joint use of a technology exhibiting decreasing marginal returns. The incentives compatibility criterion we adopt is that of strategy-proofness (SP), arguably the most robust and the most demanding incentives requirement.
We first show that no strategy-proof mechanism is efficient. We then characterize the class of strategy-proof mechanisms in the two-agent case, and show that it is the union of the serial and reverse serial families of sharing rules. Moreover, SP and the requirement that no individual benefits from the presence of others (the familiar stand-alone test) characterize the class of rules known as fixed path methods (FPMs), which is a subset of the serial family. FPMs share marginal increments of input, and the corresponding increments of output, along a predetermined path.
Finally, we consider a situation where a number of individuals form a partnership and contribute capital and labor to the enterprise. We propose a strategy-proof mechanism which improves upon autarky: the inverse marginal product proportions (IMPP) mechanism. At the margin, capital that would be left idle in autarky, but not under the efficient use of the total capital, is assigned to the agents with relatively low disutility of effort in proportion to the relative productivity of their own capital. The IMPP mechanism is effectively an FPM whose path is uniquely determined by the capital contributions of the partners. Thus, we establish a correspondence between the class of FPMs to manage a common property technology and the family of partnership problems. We discuss the appeal of the IMPP mechanism as an alternative to existing profit-sharing schemes in professional partnerships.