arXiv subjects

Yingkai Li

Publications and source records attributed to Yingkai Li.

At least 37 records · Page 2Linked to original sources

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 $Θ(\frac{n}α)$ in an environment with $n$ original bidders under the slightly stronger assumption of $α$-strong regularity, in contrast to the standard regularity assumption in the literature, which requires $Ω(n \cdot \ln \frac{m}{n})$ 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

Approximate Optimality of Linear Contracts Under Uncertainty

We consider a hidden-action principal-agent model, in which actions require different amounts of effort, and the agent privately knows his ability that determines his cost of effort. We show that linear contracts admit approximation guarantees that improve with a natural metric that captures the degree of uncertainty in the contracting setting. We thus show that linear contracts are near-optimal whenever there is enough uncertainty. In contrast, other simple contract formats such as debt contracts may suffer from a loss linear in the number of possible actions, even when there is sufficient uncertainty.

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

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

Selling Data to an Agent with Endogenous Information

We consider a model of a data broker selling information to a single agent to maximize his revenue. The agent has a private valuation of the additional information, and upon receiving the signal from the data broker, the agent can conduct her own experiment to refine her posterior belief on the states with additional costs. To maximize expected revenue, only offering full information in general is suboptimal, and the optimal mechanism may contain a continuum of menu options with partial information to prevent the agent from having incentives to acquire additional information from other sources. However, our main result shows that the additional benefit from price discrimination is limited, i.e., posting a deterministic price for revealing full information obtains at least half of the optimal revenue for arbitrary prior and cost functions.

econ.TH↗

arXiv2023

Your College Dorm and Dormmates: Fair Resource Sharing with Externalities

We study a fair resource sharing problem, where a set of resources are to be shared among a group of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, who share the same resource with them. Clearly, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even deciding the existence of such a strongly envy-free assignment is an intractable problem. Hence, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved. Under this relaxed notion, an agent envies another only when they envy both the resource and the mates of the other agent. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dormmates. We show that when the capacity of each dorm is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment. Nevertheless, the result breaks immediately when the capacity increases to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the utility guarantees of (Pareto) envy-free assignments in our model.

cs.GT↗

arXiv2023

Optimal Scoring Rules for Multi-dimensional Effort

This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest, Krysta, and Vöcking, 2005, Singer, 2010) and it is foundational to applying algorithmic mechanism design to the classroom. The paper identifies two simple families of scoring rules that guarantee constant approximations to the optimal scoring rule. The truncated separate scoring rule is the sum of single dimensional scoring rules that is truncated to the bounded range of feasible scores. The threshold scoring rule gives the maximum score if reports exceed a threshold and zero otherwise. Approximate optimality of one or the other of these rules is similar to the bundling or selling separately result of Babaioff, Immorlica, Lucier, and Weinberg (2014). Finally, we show that the approximate optimality of the best of those two simple scoring rules is robust when the agent's choice of effort is made sequentially.

cs.GT↗

arXiv2022

Making Auctions Robust to Aftermarkets

A prevalent assumption in auction theory is that the auctioneer has full control over the market and that the allocation she dictates is final. In practice, however, agents might be able to resell acquired items in an aftermarket. A prominent example is the market for carbon emission allowances. These allowances are commonly allocated by the government using uniform-price auctions, and firms can typically trade these allowances among themselves in an aftermarket that may not be fully under the auctioneer's control. While the uniform-price auction is approximately efficient in isolation, we show that speculation and resale in aftermarkets might result in a significant welfare loss. Motivated by this issue, we consider three approaches, each ensuring high equilibrium welfare in the combined market. The first approach is to adopt smooth auctions such as discriminatory auctions. This approach is robust to correlated valuations and to participants acquiring information about others' types. However, discriminatory auctions have several downsides, notably that of charging bidders different prices for identical items, resulting in fairness concerns that make the format unpopular. Two other approaches we suggest are either using posted-pricing mechanisms, or using uniform-price auctions with anonymous reserves. We show that when using balanced prices, both these approaches ensure high equilibrium welfare in the combined market. The latter also inherits many of the benefits from uniform-price auctions such as price discovery, and can be introduced with a minor modification to auctions currently in use to sell carbon emission allowances.

econ.TH↗

arXiv2022

Simple Mechanisms for Agents with Non-linear Utilities

We show that economic conclusions derived from Bulow and Roberts (1989) for linear utility models approximately extend to non-linear utility models. Specifically, we quantify the extent to which agents with non-linear utilities resemble agents with linear utilities, and we show that the approximation of mechanisms for agents with linear utilities approximately extend for agents with non-linear utilities. We illustrate the framework for the objectives of revenue and welfare on non-linear models that include agents with budget constraints, agents with risk aversion, and agents with endogenous valuations. We derive bounds on how much these models resemble the linear utility model and combine these bounds with well-studied approximation results for linear utility models. We conclude that simple mechanisms are approximately optimal for these non-linear agent models.

cs.GT↗

arXiv2021

Almost (Weighted) Proportional Allocations for Indivisible Chores

In this paper, we study how to fairly allocate m indivisible chores to n (asymmetric) agents. We consider (weighted) proportionality up to any item (PROPX) and show that a (weighted) PROPX allocation always exists and can be computed efficiently. For chores, we argue that PROPX might be a more reliable relaxation for proportionality by the facts that any PROPX allocation ensures 2-approximation of maximin share (MMS) fairness [Budish, 2011] for symmetric agents and of anyprice share (APS) fairness [Babaioff et al, 2021] for asymmetric agents. APS allocations for chores have not been studied before the current work, and our result implies a 2-approximation algorithm. Another by-product result is that an EFX and a weighted EF1 allocation for indivisible chores exist if all agents have the same ordinal preference, which might be of independent interest. We then consider the partial information setting and design algorithms that only use agents' ordinal preferences to compute approximately PROPX allocations. Our algorithm achieves a 2-approximation for both symmetric and asymmetric agents, and the approximation ratio is optimal. Finally, we study the price of fairness (PoF), i.e., the loss in social welfare by enforcing allocations to be (weighted) PROPX. We prove that the tight ratio for PoF is Theta(n) for symmetric agents and unbounded for asymmetric agents.

cs.GT↗

arXiv2021

Revelation Gap for Pricing from Samples

This paper considers prior-independent mechanism design, in which a single mechanism is designed to achieve approximately optimal performance on every prior distribution from a given class. Most results in this literature focus on mechanisms with truthtelling equilibria, a.k.a., truthful mechanisms. Feng and Hartline (2018) introduce the revelation gap to quantify the loss of the restriction to truthful mechanisms. We solve a main open question left in Feng and Hartline (2018); namely, we identify a non-trivial revelation gap for revenue maximization. Our analysis focuses on the canonical problem of selling a single item to a single agent with only access to a single sample from the agent's valuation distribution. We identify the sample-bid mechanism (a simple non-truthful mechanism) and upper-bound its prior-independent approximation ratio by 1.835 (resp. 1.296) for regular (resp. MHR) distributions. We further prove that no truthful mechanism can achieve prior-independent approximation ratio better than 1.957 (resp. 1.543) for regular (resp. MHR) distributions. Thus, a non-trivial revelation gap is shown as the sample-bid mechanism outperforms the optimal prior-independent truthful mechanism. On the hardness side, we prove that no (possibly non-truthful) mechanism can achieve prior-independent approximation ratio better than 1.073 even for uniform distributions.

cs.GT↗

arXiv2021

Equilibrium Behaviors in Repeated Games

We examine a patient player's behavior when he can build reputations in front of a sequence of myopic opponents. With positive probability, the patient player is a commitment type who plays his Stackelberg action in every period. We characterize the patient player's action frequencies in equilibrium. Our results clarify the extent to which reputations can refine the patient player's behavior and provide new insights to entry deterrence, business transactions, and capital taxation. Our proof makes a methodological contribution by establishing a new concentration inequality.

econ.TH↗

arXiv2021

Tight Regret Bounds for Infinite-armed Linear Contextual Bandits

Linear contextual bandit is an important class of sequential decision making problems with a wide range of applications to recommender systems, online advertising, healthcare, and many other machine learning related tasks. While there is a lot of prior research, tight regret bounds of linear contextual bandit with infinite action sets remain open. In this paper, we address this open problem by considering the linear contextual bandit with (changing) infinite action sets. We prove a regret upper bound on the order of $O(\sqrt{d^2T\log T})\times \text{poly}(\log\log T)$ where $d$ is the domain dimension and $T$ is the time horizon. Our upper bound matches the previous lower bound of $Ω(\sqrt{d^2 T\log T})$ in [Li et al., 2019] up to iterated logarithmic terms.

stat.ML↗

arXiv2020

Misspecified Beliefs about Time Lags

We examine the long-term behavior of a Bayesian agent who has a misspecified belief about the time lag between actions and feedback, and learns about the payoff consequences of his actions over time. Misspecified beliefs about time lags result in attribution errors, which have no long-term effect when the agent's action converges, but can lead to arbitrarily large long-term inefficiencies when his action cycles. Our proof uses concentration inequalities to bound the frequency of action switches, which are useful to study learning problems with history dependence. We apply our methods to study a policy choice game between a policy-maker who has a correctly specified belief about the time lag and the public who has a misspecified belief.

econ.TH↗

arXiv2020

Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility

The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.

cs.GT↗

arXiv2020

Benchmark Design and Prior-independent Optimization

This paper compares two leading approaches for robust optimization in the models of online algorithms and mechanism design. Competitive analysis compares the performance of an online algorithm to an offline benchmark in worst-case over inputs, and prior-independent mechanism design compares the expected performance of a mechanism on an unknown distribution (of inputs, i.e., agent values) to the optimal mechanism for the distribution in worst case over distributions. For competitive analysis, a critical concern is the choice of benchmark. This paper gives a method for selecting a good benchmark. We show that optimal algorithm/mechanism for the optimal benchmark are equal to the prior-independent optimal algorithm/mechanism. We solve a central open question in prior-independent mechanism design, namely we identify the prior-independent revenue-optimal mechanism for selling a single item to two agents with i.i.d. and regularly distributed values. Via this solution and the above equivalence of prior-independent mechanism design and competitive analysis (a.k.a. prior-free mechanism design) we show that the standard method for lower bounds of prior-free mechanisms is not generally tight for the benchmark design program.

cs.GT↗