Income Pools for Superstar Markets
针对超级明星市场中收入高度不确定的问题，提出收入池合约，通过数学模型证明其稳定性，并以棒球运动员数据表明可提升社会福利20%-30%。
“Superstar” markets, where a small portion of individuals earn disproportionately high incomes, are common in fields like entrepreneurship, sports, and entertainment. Participants in these markets face significant income uncertainty, which can deter entry or prompt early exit. To address this difficulty, we propose income pools: contracts where individuals agree to share a portion of future earnings with pool members if a specific salary milestone is achieved. To date, hundreds of income pool contracts have been signed in practice. This paper develops the first mathematical model to analyze such contracts, focusing on stability (i.e., pools where no agents leave or join). When constrained to creating a single pool, we show that a stable pool always exists with specific structural properties. Generally, stronger agents tend to be more “collaborative” and favor larger pools, whereas weaker agents are more “selfish” and prefer smaller pools. Next, we analyze pools that adhere to a maximum size (mirroring current practice) and show that stability persists. These pools typically require more weaker agents than strong ones and we find an interesting “Pareto dominance” result, whereby all agents in a stable pool prefer a particular unique stable pool. Finally, we study general partition structures, prove that a stable partition always exists under certain conditions, and provide an algorithm to construct such a partition. We conclude with a case study on data from 2,000 professional baseball players to demonstrate a 20%–30% increase in social welfare if players join income pools, under varying contract parameters. This paper was accepted by Victor Martinez de Albeniz, operations management. Funding: T. C. Y. Chan received funding support from the Natural Sciences and Engineering Research Council of Canada. N. Chen has no funding sources to report. C. Fernandes received funding support from the Natural Sciences and Engineering Research Council of Canada and the TD Management Data and Analytics Lab. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.07480 .