Mechanism Parameter Optimization under Behavioral Uncertainty via Sequential Experimental Design

In strategic environments, mechanism parameter optimization is important but challenging because the designer must choose parameters, such as auction reserve prices, to maximize a design objective while the optimal choice depends on unknown strategic behavior. The high cost of collecting strategic behavioral data limits the number of available experiments, making it difficult to simultaneously reduce behavioral uncertainty and optimize mechanism parameters. We propose a framework to address this. First, we leverage large language models to generate a pool of candidate parametric behavioral models, without requiring it to contain the true behavioral model. This converts open-ended behavioral uncertainty into a finite pool of behavioral hypotheses. Given this pool, we develop two sequential experimental design solutions to optimize mechanism parameters. The first follows a two-stage approach that selects experiments solely to reduce uncertainty about the behavioral model pool before optimizing the mechanism parameter. The second takes an end-to-end approach that selects experiments to directly reduce uncertainty about the optimal mechanism parameter. To reduce computational complexity, we approximate this experiment selection criterion using a surrogate parameter space. We further provide a theoretical guarantee that the approximation preserves the ranking of experimental designs under suitable conditions. Experiments in two strategic scenarios (static first-price auctions and dynamic pay-per-bid auctions) demonstrate that our methods consistently outperform multiple classes of baselines in mechanism parameter optimization.