We study the problem of designing mechanisms when agents' valuation functions are drawn from unknown and correlated prior distributions. In particular, we are given a prior distribution D, and we are interested in designing a (truthful) mechanism that has good performance for all "true distributions" that are close to Din Total Variation (TV) distance. We show that DSIC and BIC mechanisms in this setting are strongly robust with respect to TV distance, for any bounded objective function O, extending a recent result of Brustle et al. ([BCD20], EC 2020). At the heart of our result is a fundamental duality property of total variation distance. As direct applications of our result, we (i) demonstrate how to find approximately revenue-optimal and approximately BIC mechanisms for weakly dependent prior distributions; (ii) show how to find correlation-robust mechanisms when only "noisy" versions of marginals are accessible, extending recent results of Bei et.

For environments with large time horizons, we show that the principal's optimal

As concerns about data privacy continue to grow, differential privacy (DP) has emerged as a fundamental concept that aims to guarantee privacy by ensuring individuals' indistinguishability in data analysis. Local differential privacy (LDP) is a rigorous type of DP that requires individual data to be privatized before being sent to the collector, thus removing the need for a trusted third party to collect data. Among the numerous (L)DP-based approaches, functional DP has gained considerable attention in the DP community because it connects DP to statistical decision-making by formulating it as a hypothesis-testing problem and also exhibits Gaussian-related properties. However, the utility of privatized data is generally lower than that of non-private data, prompting research into optimal mechanisms that maximize the statistical utility for given privacy constraints. In this study, we investigate how functional LDP preserves the statistical utility by analyzing minimax risks of univariate mean estimation as well as nonparametric density estimation. We leverage the contraction property of functional LDP mechanisms and classical information-theoretical bounds to derive private minimax lower bounds. Our theoretical study reveals that it is possible to establish an interpretable, continuous balance between the statistical utility and privacy level, which has not been achieved under the $\epsilon$-LDP framework. Furthermore, we suggest minimax optimal mechanisms based on Gaussian LDP (a type of functional LDP) that achieve the minimax upper bounds and show via a numerical study that they are superior to the counterparts derived under $\epsilon$-LDP. The theoretical and empirical findings of this work suggest that Gaussian LDP should be considered a reliable standard for LDP.

We study Bayesian automated mechanism design in unstructured dynamic environments, where a principal repeatedly interacts with an agent, and takes actions based on the strategic agent's report of the current state of the world. Both the principal and the agent can have arbitrary and potentially different valuations for the actions taken, possibly also depending on the actual state of the world. Moreover, at any time, the state of the world may evolve arbitrarily depending on the action taken by the principal. The goal is to compute an optimal mechanism which maximizes the principal's utility in the face of the self-interested strategic agent.We give an efficient algorithm for computing optimal mechanisms, with or without payments, under different individual-rationality constraints, when the time horizon is constant. Our algorithm is based on a sophisticated linear program formulation, which can be customized in various ways to accommodate richer constraints.

We build a mechanism design framework where a platform designs GenAI models to screen users who obtain instrumental value from the generated conversation and privately differ in their preference for latency. We show that the revenue-optimal mechanism is simple: deploy a single aligned (user-optimal) model and use token cap as the only instrument to screen the user. The design decouples model training from pricing, is readily implemented with token metering, and mitigates misalignment pressures.

Such concerns are shared by politics and industry, leading to the adoption of France's "Loi pour une République numérique (Law for the Digital Republic)" in October 2016 (Algan et al., 2016), EU's General Data Protection Regulation in May 2018, and the California Consumer Privacy Act (Wang et al., 2022), all of which regulate data protection, collection, and processing.