GreedyBM: Greedy Utility Discovery for Automated Modeling of Human Strategic Behavior

Predicting human strategic behavior requires models that capture systematic departures from individual payoff maximization. Random utility models address this need by separating systematic utility from stochastic influences, but specifying the systematic utility typically demands substantial domain expertise and extensive manual refinement. We introduce GreedyBM, a method that constructs systematic utilities greedily, adding one term at a time, with each term encoding an interpretable behavioral tendency. At each stage, GreedyBM prompts a large language model (LLM) to propose candidate terms based on the current systematic utility and on previously evaluated candidates, and then adds the highest-scoring one. We derive a computable lower bound on the training negative log-likelihood (NLL) reduction achieved in a single stage, together with a multi-stage bound that relates candidate quality to the attainable training NLL. Across three strategic scenarios (the Ultimatum Game, repeated rock–paper–scissors, and continuous double auctions), GreedyBM achieves a lower mean test NLL than both expert-designed models and models discovered by existing LLM-based methods, while consuming substantially fewer tokens during search.