Mechanism Design - Learning Resources

Contracting for LLM Delegation: Moral Hazard in Technology and Effort Choice

We extend the standard Principal-Agent framework to scenarios where the Agent selects from a suite of technologies, each characterized by a distinct cost-capability profile. This framework is increasingly critical in the era of Large Language Models (LLMs), where Agents choose both a model and an associated effort level (e.g., token budget). We model the relationship between output quality and effort as a concave, saturating function, which depends on the Agent's hidden two-dimensional action choice balancing technology selection and effort allocation. We derive the optimal linear contract for the Principal, demonstrating that the Agent's best response is characterized by a threshold reward share that triggers technology switching. Finally, we calibrate our model using open-weight LLM pairings across the MATH and MMLUPro benchmarks. We show that both Principal and Agent, when employing bandit algorithms to navigate this environment, converge to strategies that closely align with our theoretical equilibrium. These results suggest that simple linear contracts can effectively incentivize complex, technology-aware delegation in agentic workflows.

Stackelberg Mean Field Games: convergence and existence results to the problem of Principal with multiple Agents in competition

In a situation of moral hazard, this paper investigates the problem of Principal with $n$ Agents when the number of Agents $n$ goes to infinity. There is competition between the Agents expressed by the fact that they optimize their utility functions through a Nash equilibrium criterion. Each Agent is offered by the Principal a contract which is divided into a Markovian part involving the state/production of the Agent and a non--Markovian part involving the states/productions of all the other Agents. The Agents are in interactions. These interactions are characterized by common noise, the empirical distribution of states/productions and controls, and the contract which is not assumed to be a map of the empirical distribution. By the help of the mean field games theory, we are able to formulate an appropriate $limit$ problem involving a Principal with a $representative$ Agent. We start by solving the problem of both the Principal and the $representative$ Agent in this $limit$ problem. Then, when $n$ goes to infinity, we show that the problem of Principal with $n$ Agents converges to the $limit$ problem of Principal with a $representative$ Agent. A notable result is that, despite allowing a general type of contracts, it is approximately optimal for the Principal to offer contracts to the $n$ Agents that are maps of the empirical distribution of states/productions and controls of the Agents.

Scalable Neural Incentive Design with Parameterized Mean-Field Approximation

Designing incentives for a multi-agent system to induce a desirable Nash equilibrium is both a crucial and challenging problem appearing in many decision-making domains, especially for a large number of agents $N$. Under the exchangeability assumption, we formalize this incentive design (ID) problem as a parameterized mean-field game (PMFG), aiming to reduce complexity via an infinite-population limit. We first show that when dynamics and rewards are Lipschitz, the finite-$N$ ID objective is approximated by the PMFG at rate $\mathcal{O}(\frac{1}{\sqrt{N}})$. Moreover, beyond the Lipschitz-continuous setting, we prove the same $\mathcal{O}(\frac{1}{\sqrt{N}})$ decay for the important special case of sequential auctions, despite discontinuities in dynamics, through a tailored auction-specific analysis. Built on our novel approximation results, we further introduce our Adjoint Mean-Field Incentive Design (AMID) algorithm, which uses explicit differentiation of iterated equilibrium operators to compute gradients efficiently. By uniting approximation bounds with optimization guarantees, AMID delivers a powerful, scalable algorithmic tool for many-agent (large $N$) ID. Across diverse auction settings, the proposed AMID method substantially increases revenue over first-price formats and outperforms existing benchmark methods.

A tale of a Principal and many many Agents

In this paper, we investigate a moral hazard problem in finite time with lump$-$sum and continuous payments, involving infinitely many Agents with mean field type interactions, hired by one Principal. By reinterpreting the mean$-$field game faced by each Agent in terms of a mean field forward backward stochastic differential equation (FBSDE for short), we are able to rewrite the Principal's problem as a control problem of McKean$-$Vlasov SDEs. We review one general approache to tackle it, introduced recently in [1, 43, 44, 45, 46] using dynamic programming and Hamilton$-$Jacobi$-$Bellman (HJB for short) equations, and mention a second one based on the stochastic Pontryagin maximum principle, which follows [10]. We solve completely and explicitly the problem in special cases, going beyond the usual linear$-$quadratic framework. We finally show in our examples that the optimal contract in the $N-$players' model converges to the mean$-$field optimal contract when the number of agents goes to $+\infty$, thus illustrating in our specific setting the general results of [8].

Heterogeneous participation and allocation skews: when is choice "worth it"?

A core ethos of the Economics and Computation (EconCS) community is that people have complex private preferences and information of which the central planner is unaware, but which an appropriately designed mechanism can uncover to improve collective decisionmaking. This ethos underlies the community's largest deployed success stories, from stable matching systems to participatory budgeting. I ask: is this choice and information aggregation ``worth it''? In particular, I discuss how such systems induce \textit{heterogeneous participation}: those already relatively advantaged are, empirically, more able to pay time costs and navigate administrative burdens imposed by the mechanisms. I draw on three case studies, including my own work -- complex democratic mechanisms, resident crowdsourcing, and school matching. I end with lessons for practice and research, challenging the community to help reduce participation heterogeneity and design and deploy mechanisms that meet a ``best of both worlds'' north star: \textit{use preferences and information from those who choose to participate, but provide a ``sufficient'' quality of service to those who do not.}

Public Persuasion with Endogenous Fact-Checking

We study public persuasion when a sender communicates with a large audience that can fact-check at heterogeneous costs. The sender commits to a public information policy before the state is realized, but any verifiable claim she makes after observing the state must be truthful (an ex-post implementability constraint). Receivers observe the public message and then decide whether to verify; this selective verification feeds back into the sender's objective and turns the design problem into a constrained version of Bayesian persuasion. Our main result is a reverse comparative static: when fact-checking becomes cheaper in the population, the sender optimally supplies a strictly less informative public signal. Intuitively, cheaper verification makes bold claims invite scrutiny, so the sender coarsens information to dampen the incentive to verify. We also endogenize two ex-post instruments - continuous falsification and fixed-cost repression - and characterize threshold substitutions from persuasion to manipulation and, ultimately, to repression as monitoring improves. The framework provides testable predictions for how transparency, manipulation, and repression co-move with changes in verification technology.

Online Learning in a Creator Economy

The creator economy is revolutionizing the way in which individuals can profit from their engagement with online platforms. In this paper, we initiate the formal study of online learning in a creator economy by modeling it as a three-party game between users, a platform, and content creators. The platform interacts with creators through contracts under a principal-agent framework and with users via a recommender system. We study how the platform can jointly optimize contracts and recommendation policies in an online learning setting. We analyze return-based and feature-based contracts. Under smoothness assumptions, return-based contracts achieve regret \Theta(T^2/3). For feature-based contracts, we introduce an intrinsic dimension d and prove a regret bound \mathcalO(T^(d+1)/(d+2)), which is tight for linear families.

Information and Contract Design for Repeated Interactions between...

We study the consequences of information asymmetries and misaligned incentives in settings with multiple independent agents. We model an interaction between a Sender, who holds vital private...

An Interpretable Automated Mechanism Design Framework with Large Language Models

Mechanism design has long been a cornerstone of economic theory, with traditional approaches relying on mathematical derivations. Recently, automated approaches, including differentiable economics with neural networks, have emerged for designing payments and allocations. While both analytical and automated methods have advanced the field, they each face significant weaknesses: mathematical derivations are not automated and often struggle to scale to complex problems, while automated and especially neural-network-based approaches suffer from limited interpretability. To address these challenges, we introduce a novel framework that reformulates mechanism design as a code generation task. Using large language models (LLMs), we generate heuristic mechanisms described in code and evolve them to optimize over some evaluation metrics while ensuring key design criteria (e.g., strategy-proofness) through a problem-specific fixing process. This fixing process ensures any mechanism violating the design criteria is adjusted to satisfy them, albeit with some trade-offs in performance metrics. These trade-offs are factored in during the LLM-based evolution process. The code generation capabilities of LLMs enable the discovery of novel and interpretable solutions, bridging the symbolic logic of mechanism design and the generative power of modern AI. Through rigorous experimentation, we demonstrate that LLM-generated mechanisms achieve competitive performance while offering greater interpretability compared to previous approaches. Notably, our framework can rediscover existing manually designed mechanisms and provide insights into neural-network based solutions through Programming-by-Example. These results highlight the potential of LLMs to not only automate but also enhance the transparency and scalability of mechanism design, ensuring safe deployment of the mechanisms in society.

Deep mechanism design: Learning social and economic policies for human benefit

Human society is coordinated by mechanisms that control how prices are agreed, taxes are set, and electoral votes are tallied. The design of robust and effective mechanisms for human benefit is a core problem in the social, economic, and political sciences. Here, we discuss the recent application of modern tools from AI research, including deep neural networks trained with reinforcement learning (RL), to create more desirable mechanisms for people. We review the application of machine learning to design effective auctions, learn optimal tax policies, and discover redistribution policies that win the popular vote among human users. We discuss the challenge of accurately modeling human preferences and the problem of aligning a mechanism to the wishes of a potentially diverse group. We highlight the importance of ensuring that research into “deep mechanism design” is conducted safely and ethically.

A Collectivist, Economic Perspective on AI

Information technology is in the midst of a revolution in which omnipresent data collection and machine learning are impacting the human world as never before. The word ``intelligence'' is being used as a North Star for the development of this technology, with human cognition viewed as a baseline. This view neglects the fact that humans are social animals and that much of our intelligence is social and cultural in origin. Moreover, failing to properly situate aspects of intelligence at the social level contributes to the treatment of the societal consequences of technology as an afterthought. The path forward is not merely more data and compute, and not merely more attention paid to cognitive or symbolic representations, but a thorough blending of economic and social concepts with computational and inferential concepts at the level of algorithm design.

DIMACS :: Details

« IBM/DIMACS/DATA-INSPIRE Workshop on Bridging Game Theory and Machine Learning for Multi-party Decision Making