Mechanism Design

The data market design problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price [Bergemann et al., 2018]. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others [Bonatti et al., 2022]. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design [Dütting et al., 2023], we must learn signaling schemes rather than allocation rules and handle obedience constraints $-$ these arising from modeling the downstream actions of buyers $-$ in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

Algorithmic recourse promises to help applicants rejected by automated systems by explaining the changes needed to secure acceptance. What incentive do decision-makers, such as banks and employers, have to offer recourse? We study this question in a screening model in which recourse is both productive and selective: completing recourse improves an applicant's value to the decision-maker, but applicants differ in their cost of completion. The optimal policy is a threshold rule: reject applicants with low scores, offer recourse to an intermediate range of scores, and accept applicants with high scores outright. Because the intermediate range spans the cutoff that would separate acceptance from rejection when recourse is not available, some marginal applicants gain a new path to acceptance, while others---who would have been accepted outright---must now clear a costly hurdle.

Many real-world domains--including e-commerce platform design, security planning, and multi-agent coordination--feature leader-follower problems where one decision-maker commits to a policy and others react strategically. We develop a reinforcement learning framework for such interactions in sequential environments with partial observations and multiple followers. Followers may adapt through no-regret learning or reinforcement learning, potentially departing from equilibrium behavior. The framework embeds follower adaptation into the leader's environment to construct a single-agent partially observable Markov decision process--the Stackelberg POMDP. For policy-interactive response algorithms, which access the leader's policy through queries, we prove that an optimal policy based only on the leader's game history yields an optimal commitment under the specified response procedure. We use proximal policy optimization with a centralized critic and train contextual meta-followers to respond across leader policies. In indirect mechanism design, mechanisms using buyer messages achieve higher social welfare than optimal standard sequential price mechanisms across all tested type counts, with responses certified as approximate Bayesian coarse correlated equilibria. In platform design, learned display rules increase mean consumer surplus by 8.4% over an optimized fixed price cap while accommodating hidden seller costs. In Atari bilateral trade, meta-learned follower responses support joint learning of visual gameplay and economic decisions; assigning leadership to the seller or buyer shifts transaction prices and payoffs in that agent's favor. Controlled ablations examine how response credit, policy consistency, and reward timing affect learning.