arXiv subjects

Yingkai Li

Publications and source records attributed to Yingkai Li.

At least 19 recordsLinked to original sources

arXiv2026

Robust Aggregation of Calibrated Forecasts

Decision-makers often rely on multiple probabilistic forecasts that are individually calibrated but need not be fully informative. We develop a framework for aggregating such forecasts when the decision-maker knows only that experts satisfy calibration. We show that the joint distribution of calibrated forecasts can contain decision-relevant information that is unavailable from any single expert, so the standard optimal-in-hindsight (OIH) benchmark may substantially understate attainable performance. To formalize this idea, we introduce a robust max-min benchmark: the best payoff a decision-maker can guarantee against all profile-wise conditional-mean mappings compatible with calibration. This benchmark is tractable, admits a linear-programming formulation, and dominates the OIH benchmark up to calibration error. It can nevertheless be strictly below the Bayesian benchmark, clarifying the value of knowing experts' information structures. Finally, we provide online algorithms that attain the robust benchmark under forecast-only feedback and stronger contextual benchmarks under state feedback.

econ.TH↗

arXiv2026

Strict Fairness at What Cost? Envy-Free Contracts with Subsidies

We study algorithmic fair contract design, where a principal designs task-level contracts and fairly delegates a set of tasks to a set of agents. Prior work reveals a fairness-revenue dilemma: exact envy-free (EF) contracts may have an unbounded price of fairness (PoF), while approximate notions avoid this unboundedness only by weakening strict fairness. To address this dilemma, we propose a novel scheme, called {\it Envy-free Contracts with Subsidies} (EFS), in which the principal may additionally offer agent-specific subsidies to restore strict fairness. Our main technical result is a tight characterization of the price of fairness for EFS contracts. In sharp contrast to EF contracts, whose PoF can be unbounded, we show that the PoF of EFS contracts is $n^{n+O(1)}$, where $n$ is the number of agents. Moreover, EFS contracts can outperform EF contracts by an arbitrarily large factor in terms of the principal's revenue. Finally, we present the complexity landscape: computing optimal EFS contracts is NP-hard in general, whereas a polynomial-time algorithm exists when the number of tasks is constant.

cs.GT↗

arXiv2026

Going Public: Communication in Collective Decisions

A principal and $n\ge 2$ agents can launch a project if the principal proposes it and at least $k$ agents accept. Their individual payoffs from the project depend on an ex ante unknown state. The principal can conduct a test to learn about the state and then communicate her findings to the agents via cheap talk. This paper focuses on comparing two communication regimes: public and private messaging. We show that public messaging is weakly dominant: any outcome implementable under private messaging can also be implemented under public messaging. Moreover, in a canonical environment with linear payoffs, we characterize the principal's optimal test in each regime and show that public messaging can be strictly dominant if and only if there exist two agents who are the principal's conflicting allies.

econ.TH↗

arXiv2026

Allocating Resources under Strategic Misrepresentation

We study how to allocate resources to participants who can strategically misrepresent their deservingness at a cost. A principal assigns item(s) (or money) among multiple agents on the basis of their costly signals. Each agent's signal reflects their private type in the absence of misrepresentation but can be inflated above their true type at a cost. The principal is a social planner who aims to maximize the weighted average of matching efficiency and a utilitarian objective. Strategic misrepresentation introduces novel incentive-compatibility constraints, under which we characterize the optimal mechanism. We apply our characterization to two kinds of markets, distinguished by resource scarcity, and show that the principal strictly benefits from randomizing the allocations based on costly signals when the population of participants is large enough. Interestingly, in large markets with scarce resources, the format of the optimal mechanism converges to a winner-takes-all contest; however, there is a non-diminishing value in randomizing allocations to middle types as the population of participants grows.

econ.TH↗

arXiv2026

Anonymous Pricing in Large Markets

We study revenue maximization when a seller offers $k$ identical units to ex ante heterogeneous, unit-demand buyers. While anonymous pricing can be $\Theta(\log k)$ worse than optimal in general multi-unit environments, we show that this pessimism disappears in large markets, where no single buyer accounts for a non-negligible share of optimal revenue. Under (quasi-)regularity, anonymous pricing achieves a $2+O(1/\sqrt{k})$ approximation to the optimal mechanism; the worst-case ratio is maximized at about $2.47$ when $k=1$ and converges to $2$ as $k$ grows. This indicates that the gains from third-degree price discrimination are mild in large markets.

cs.GT↗

arXiv2026

Screening for Choice Sets

We study a screening problem in which an agent privately knows which actions or technologies are feasible and can disclose only a subset to a principal. Once disclosed, feasible options are verifiable and their payoff consequences are publicly known, so private information concerns feasibility rather than payoffs, misreporting restricts the principal's choices directly rather than distorting her beliefs. Assuming feasible sets are ordered by inclusion, we establish a simple characterization of the optimal mechanism, where the principal either behaves as if there is no asymmetric information or locally provides no reward for better proposals. We derive comparative statics and illustrate the framework in applications to managing persuasion, action elicitation, and production-technology elicitation.

econ.TH↗

arXiv2025

Fair Team Contracts

A principal selects a team of agents for collaborating on a joint project. The principal aims to design a revenue-optimal contract that incentivizes the team of agents to exert costly effort while satisfying fairness constraints. We show that the optimal fair contract ensures that there is a minimum share, and every agent receives a linear contract weakly higher than the minimum share that is sufficient to incentivize them to exert costly effort. Leveraging this structural characterization, we design an FPTAS for additive success functions and a constant approximation algorithm for submodular success functions. Moreover, we show that the optimal fair contract can outperform the non-discriminatory one by a factor $1.445$, and this bound is tight for both additive and submodular success functions.

cs.GT↗

arXiv2025

Three Tiers and Thresholds: Incentives in Private Market Investing

This paper studies optimal contract design in private market investing, focusing on internal decision making in venture capital and private equity firms. A principal relies on an agent who privately exerts costly due diligence effort and then recommends whether to invest. Outcomes are observable ex post even when an opportunity is declined, allowing compensation to reward both successful investments and prudent decisions to pass. We characterize profit maximizing contracts that induce information acquisition and truthful reporting. We show that three tier contracts are sufficient, with payments contingent on the agent's recommendation and the realized return. In symmetric environments satisfying the monotone likelihood ratio property, the optimal contract further simplifies to a threshold contract that pays only when the recommendation is aligned with an extreme realized return. These results provide guidance for performance based compensation that promotes diligent screening while limiting excessive risk taking.

cs.GT↗

arXiv2025

Scale-robust Auctions

We study auctions that are robust at any scale, i.e., they can be applied to sell both expensive and cheap items and achieve the best multiplicative approximation of the optimal revenue in the worst case. We first show that it is without loss of optimality to restrict attention to scale-invariant mechanisms whenever the family of possible distributions is closed under every positive rescaling. This conclusion uses no regularity or other distributional shape restriction. We then solve the two-agent, single-item problem with values drawn i.i.d. from an unknown regular distribution when only a high value bidder can receive a positive allocation. The robustly optimal mechanism in this class randomizes between the second-price auction, with probability approximately 0.806, and a markup auction that offers the item to the highest-valued bidder at a price equal to 2.447 times the second-highest value. Its worst-case approximation ratio is approximately 1.907.

cs.GT↗

arXiv2025

Algorithmic Fair Contracts

We initiate the algorithmic study of fair contract design. A principal assigns multiple tasks to heterogeneous agents and chooses task-level linear contracts; agents differ in costs and success probabilities, and fairness requires each agent to prefer her own task-contract bundle to any other agent's. Unlike envy-free allocations of indivisible items, envy-free full-allocation contracts always exist, but optimizing revenue under this constraint is computationally difficult: no polynomial-time algorithm can achieve any constant-factor approximation in general. We therefore identify tractable regimes. With a constant number of tasks, optimal EF, EF1, and $\epsilon$-EF contracts are computable in polynomial time. With a constant number of agents, exact EF remains hard, even for three agents, while EF1 and $\epsilon$-EF admit additive FPTAS against the EF benchmark. We also show that exact EF can have an unbounded price of fairness, whereas $\epsilon$-EF and EF1 can restore bounded revenue loss.

cs.GT↗

arXiv2025

Competition Complexity in Multi-Item Auctions: Beyond VCG and Regularity

We quantify the value of the monopoly's bargaining power in terms of competition complexity--that is, the number of additional bidders the monopoly must attract in simple auctions to match the expected revenue of the optimal mechanisms (c.f., Bulow and Klemperer, 1996, Eden et al., 2017)--within the setting of multi-item auctions. We show that for simple auctions that sell items separately, the competition complexity is $\Theta(\frac{n}{\alpha})$ in an environment with $n$ original bidders under the slightly stronger assumption of $\alpha$-strong regularity, in contrast to the standard regularity assumption in the literature, which requires $\Omega(n \cdot \ln \frac{m}{n})$ additional bidders (Feldman et al., 2018). This significantly reduces the value of learning the distribution to design the optimal mechanisms, especially in large markets with many items for sale. For simple auctions that sell items as a grand bundle, we establish a constant competition complexity bound in a single-bidder environment when the number of items is small or when the value distribution has a monotone hazard rate. Some of our competition complexity results also hold when we compete against the first best benchmark (i.e., optimal social welfare).

cs.GT↗

arXiv2025

Multi-Project Contracts

We study a new class of contract design problems where a principal delegates the execution of multiple projects to a set of agents. The principal's expected reward from each project is a combinatorial function of the agents working on it. Each agent has limited capacity and can work on at most one project, and the agents are heterogeneous, with different costs and contributions for participating in different projects. The main challenge of the principal is to decide how to allocate the agents to projects when the number of projects grows in scale. We analyze this problem under different assumptions on the structure of the expected reward functions. As our main result, for XOS functions we show how to derive a constant approximation to the optimal multi-project contract in polynomial time, given access to value and demand oracles. Along the way (and of possible independent interest), we develop approximate demand queries for \emph{capped} subadditive functions, by reducing to demand queries for the original functions. Our work paves the way to combinatorial contract design in richer settings.

cs.GT↗

arXiv2025

Multi-Dimensional Screening with Endogenous Information Disclosure

We study multi-product monopoly pricing where the seller jointly designs the selling mechanism and the information structure for the buyer to learn his values. Unlike the case with exogenous information, we show that when the seller controls information, even uniform pricing guarantees at least half of the optimal revenue. Moreover, for negatively affiliated or exchangeable value distributions, deterministic pricing is revenue-optimal. Our results highlight the power of information design in making pricing mechanisms approximately optimal in multi-dimensional settings.

cs.GT↗

arXiv2024

Dynamics and Contracts for an Agent with Misspecified Beliefs

We study a single-agent contracting environment where the agent has misspecified beliefs about the outcome distributions for each chosen action. First, we show that for a myopic Bayesian learning agent with only two possible actions, the empirical frequency of the chosen actions converges to a Berk-Nash equilibrium. However, through a constructed example, we illustrate that this convergence in action frequencies fails when the agent has three or more actions. Furthermore, with multiple actions, even computing an $\varepsilon$-Berk-Nash equilibrium requires at least quasi-polynomial time under the Exponential Time Hypothesis (ETH) for the PPAD-class. This finding poses a significant challenge to the existence of simple learning dynamics that converge in action frequencies. Motivated by this challenge, we focus on the contract design problems for an agent with misspecified beliefs and two possible actions. We show that the revenue-optimal contract, under a Berk-Nash equilibrium, can be computed in polynomial time. Perhaps surprisingly, we show that even a minor degree of misspecification can result in a significant reduction in optimal revenue.

cs.GT↗

arXiv2024

Learning and Communication Towards Unanimous Consent

A principal and an agent can launch a project under unanimous consent. Their individual payoffs from the project depend on an underlying state, and the agent privately knows his own preference. The principal can conduct a test to learn about the state and then communicate with the agent, but has limited commitment, as she may misreport her findings. We show that limited commitment makes binary tests optimal. Moreover, when players' preferences are positively aligned, the optimal test is a threshold test. When their preferences are negatively aligned, the optimal test is either an interval test or a tail test, depending on the agent's relative risk attitude. Additionally, the principal can benefit from screening the agent through a menu of tests, which admits a simple structure regardless of the complexity of the agent's type space.

econ.TH↗

arXiv2024

Algorithmic Information Disclosure in Optimal Auctions

This paper studies a joint design problem where a seller can design both the signal structures for the agents to learn their values, and the allocation and payment rules for selling the item. In his seminal work, Myerson (1981) shows how to design the optimal auction with exogenous signals. We show that the problem becomes NP-hard when the seller also has the ability to design the signal structures. Our main result is a polynomial-time approximation scheme (PTAS) for computing the optimal joint design with at most an $ε$ multiplicative loss in expected revenue. Moreover, we show that in our joint design problem, the seller can significantly reduce the information rent of the agents by providing partial information, which ensures a revenue that is at least $1 - \frac{1}{e}$ of the optimal welfare for all valuation distributions.

cs.GT↗

arXiv2023

Revenue Maximization for Buyers with Costly Participation

We study mechanisms for selling a single item when buyers have private costs for participating in the mechanism. An agent's participation cost can also be interpreted as an outside option value that she must forego to participate. This substantially changes the revenue maximization problem, which becomes non-convex in the presence of participation costs. For multiple buyers, we show how to construct a $(2+ε)$-approximately revenue-optimal mechanism in polynomial time. Our approach makes use of a many-buyers-to-single-buyer reduction, and in the single-buyer case our mechanism improves to an FPTAS. We also bound the menu size and the sample complexity for the optimal single-buyer mechanism. Moreover, we show that posting a single price in the single-buyer case is in fact optimal under the assumption that either (1) the participation cost is independent of the value, and the value distribution has decreasing marginal revenue or monotone hazard rate; or (2) the participation cost is a concave function of the value. When there are multiple buyers, we show that sequential posted pricing guarantees a large fraction of the optimal revenue under similar conditions.

cs.GT↗

arXiv2023

Incentivizing Forecasters to Learn: Summarized vs. Unrestricted Advice

How should forecasters be incentivized to acquire the most information when learning takes place over time? We address this question in the context of a novel dynamic mechanism design problem in which a designer incentivizes an expert to learn by conditioning rewards on an event's outcome and the expert's reports. Eliciting summarized advice at a terminal date maximizes information acquisition if an informative signal either fully reveals the outcome or has predictable content. Otherwise, richer reporting capabilities may be required. Our findings shed light on incentive design for consultation and forecasting by illustrating how learning dynamics shape the qualitative properties of effort-maximizing contracts.

econ.TH↗