Stochastic Resource Allocation with Endogenous Recruitment

A recent preprint on arXiv (2605.12111) presents a model for sequential resource allocation aimed at adaptive network recruitment. This model addresses the challenge of distributing a finite budget of identical resources across several rounds to individuals with uncertain referral capabilities. Successful referrals create new decision-making opportunities, while providing extra resources to an individual results in diminishing returns. The authors demonstrate that the single-round scenario can be solved exactly using a greedy approach based on marginal survival probabilities. However, the multi-round scenario faces challenges due to the complex evolution of the stochastic high-dimensional frontier. To tackle this, they introduce a population-level surrogate value function that relies solely on the remaining budget and frontier size, facilitating an exact dynamic program through truncated probability generating functions, leading to a planning algorithm with polynomial time complexity in relation to the budget and time horizon.