🤖 AI Summary
This paper addresses the problem of personalized intervention allocation in sequential games to maximize equilibrium social welfare. Given that the long-term behavior of sequentially interacting agents follows a Gibbs stationary distribution, exact modeling and optimization pose both theoretical and computational challenges. To tackle this, we propose a novel optimization framework that integrates variational approximation of the Gibbs stationary distribution with greedy policy search—yielding an individualized intervention algorithm with provable welfare regret bounds. Our method unifies variational inference, stationary equilibrium analysis, and policy optimization. Empirical evaluation on Indian microfinance data demonstrates substantial improvements in social welfare; extensive simulations and real-world validation further confirm its effectiveness, robustness, and computational feasibility.
📝 Abstract
Designing individualized allocation of treatments so as to maximize the equilibrium welfare of interacting agents has many policy-relevant applications. Focusing on sequential decision games of interacting agents, this paper develops a method to obtain optimal treatment assignment rules that maximize a social welfare criterion by evaluating stationary distributions of outcomes. Stationary distributions in sequential decision games are given by Gibbs distributions, which are difficult to optimize with respect to a treatment allocation due to analytical and computational complexity. We apply a variational approximation to the stationary distribution and optimize the approximated equilibrium welfare with respect to treatment allocation using a greedy optimization algorithm. We characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. We implement our proposed method in simulation exercises and an empirical application using the Indian microfinance data (Banerjee et al., 2013), and show it delivers significant welfare gains.
