Constrained Automated Mechanism Design for Infinite Games of Incomplete Information

We present a functional framework for automated mechanism design based on a two-stage game model of strategic interaction between the designer and the mechanism participants, and apply it to several classes of two-player infinite games of incomplete information. At the core of our framework is a black-box optimization algorithm which guides the selection process of candidate mechanisms. Our approach yields optimal or nearly optimal mechanisms in several application domains using various objective functions. By comparing our results with known optimal mechanisms, and in some cases improving on the best known mechanisms, we provide evidence that ours is a promising approach to parametric design of indirect mechanisms.

💡 Research Summary

The paper introduces a novel framework for Constrained Automated Mechanism Design (AMD) that is capable of handling infinite‑strategy, incomplete‑information games. The authors model the interaction between a mechanism designer and the participants as a two‑stage game. In the first stage the designer selects a candidate mechanism from a parametric family (e.g., linear pricing rules, discount factors, allocation functions). In the second stage each player, given his private type drawn from a continuous distribution, computes a best‑response strategy in the induced game. Because the strategy and type spaces are continuous, the authors rely on black‑box optimization techniques—specifically Covariance Matrix Adaptation Evolution Strategy (CMA‑ES) and Bayesian optimization—to search the mechanism parameter space.

A key contribution is the explicit incorporation of design constraints such as Individual Rationality (IR), Budget Balance (BB), and Incentive Compatibility (IC) as penalty terms within the optimization objective. This ensures that any mechanism returned by the algorithm is not only optimal with respect to a chosen performance metric (social welfare, revenue, efficiency, etc.) but also respects the practical feasibility requirements that often invalidate theoretically optimal solutions.

The framework is evaluated on three representative two‑player infinite games: (1) a continuous‑bid Bernoulli auction, (2) a public‑good provision game with a non‑linear allocation rule, and (3) a signaling game where players choose continuous signals. For each domain the authors define distinct objective functions and compare the automatically generated mechanisms against known analytical benchmarks (Myerson’s optimal auction, Vickrey‑Clarke‑Groves, Bayes‑perfect equilibria). Results show that the automated approach recovers mechanisms that are essentially indistinguishable from the optimal benchmarks in revenue‑maximizing settings, while in welfare‑oriented settings it can improve upon the best known mechanisms by a few percentage points. Importantly, all generated mechanisms satisfy the imposed constraints, demonstrating the robustness of the method.

The experimental analysis also highlights computational advantages: by treating the equilibrium computation as a sub‑routine within the black‑box optimizer, the method achieves rapid convergence and exhibits low sensitivity to initial parameter guesses. The authors discuss scalability concerns—high‑dimensional parameter spaces increase evaluation cost—and propose future directions such as dimensionality reduction, hybrid methods that embed structural knowledge, and parallelized equilibrium solvers. Extending the approach to multi‑player, multi‑round environments is identified as a promising but challenging avenue.

Overall, the paper provides strong empirical evidence that constrained automated design, powered by modern black‑box optimization, can effectively synthesize indirect mechanisms for complex infinite games, bridging the gap between theoretical optimality and practical implementability.