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We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean field equilibrium, and it is shown to be the limit of associated n-player games. Conversely, the mean field strategy induces n-player ε-Nash equilibria for any continuous reward function—but not for discontinuous ones. In a second part, we study the problem of a principal who can choose how to distribute a reward budget over the ranks and aims to maximize the performance of the median player. The optimal reward design (contract) is found in closed form, complementing the merely partial results available in the n-player case. We then analyze the quality of the mean field design when used as a proxy for the optimizer in the n-player game. Surprisingly, the quality deteriorates dramatically as n grows. We explain this with an asymptotic singularity in the induced n-player equilibrium distributions. Funding: M. Nutz is supported by an Alfred P. Sloan Fellowship and the Division of Mathematical Sciences of the National Science Foundation [Grants DMS-1812661 and DMS-2106056]. Y. Zhang is supported in part by the Natural Sciences and Engineering Research Council of Canada [NSERC Discovery Grant RGPIN-2020-06290]. 

Abstract Cancer immunotherapy with autologous chimeric antigen receptor (CAR) T cells faces challenges in manufacturing and patient selection that could be avoided by using ‘off-the-shelf’ products, such as allogeneic CAR natural killer T (^AlloCAR-NKT) cells. Previously, we reported a system for differentiating human hematopoietic stem and progenitor cells into^AlloCAR-NKT cells, but the use of three-dimensional culture and xenogeneic feeders precluded its clinical application. Here we describe a clinically guided method to differentiate and expand IL-15-enhanced^AlloCAR-NKT cells with high yield and purity. We generated^AlloCAR-NKT cells targeting seven cancers and, in a multiple myeloma model, demonstrated their antitumor efficacy, expansion and persistence. The cells also selectively depleted immunosuppressive cells in the tumor microenviroment and antagonized tumor immune evasion via triple targeting of CAR, TCR and NK receptors. They exhibited a stable hypoimmunogenic phenotype associated with epigenetic and signaling regulation and did not induce detectable graft versus host disease or cytokine release syndrome. These properties of^AlloCAR-NKT cells support their potential for clinical translation.