arXiv subjects

Mengfan Ma

Publications and source records attributed to Mengfan Ma.

6 recordsLinked to original sources

arXiv2026

Breaking the 4-Approximation Barrier in Strategyproof Two-Facility Location

We study strategyproof mechanism design without transfers for the two-facility location problem in metric spaces. A mechanism selects two facility locations based on agents' reported locations; each agent incurs her distance to the nearer facility, and the objective is to minimize the expected social cost. A mechanism is strategyproof if no agent ever benefits from misreporting her location. The best approximation ratio achieved by a randomized strategyproof mechanism has been $4$, attained by the Proportional mechanism of Lu, Sun, Wang, and Zhu (EC 2010), and the best lower bound has been $1.045$, due to Lu, Wang, and Zhou (WINE 2009). Neither bound has moved since then, even on the line $\mathbb{R}$. We improve both bounds. Our main result is a randomized strategyproof mechanism with approximation ratio $11/3 \approx 3.667$ on every Ptolemaic metric space, a rich class containing all Euclidean spaces. The mechanism randomizes between the Proportional mechanism and a new mechanism that we call Global Pair. Global Pair draws an unordered pair of agents with probability proportional to their distance and opens facilities at their reported locations. Although Global Pair and Proportional each have approximation ratio $4$, the two mechanisms attain their worst-case approximation ratios on complementary instances. Randomizing between them balances these complementary weaknesses and breaks the $4$-approximation barrier. On the lower-bound side, we construct a new two-profile instance that yields a lower bound of $(1+\sqrt{2})/2 \approx 1.207$, improving upon the previous lower bound of $1.045$.

cs.GT↗

arXiv2026

Searching for Optimal Prices in Two-Sided Markets

We investigate online pricing in two-sided markets where a platform repeatedly posts prices based on binary accept/reject feedback to maximize gains-from-trade (GFT) or profit. We characterize the regret achievable across three mechanism classes: Single-Price, Two-Price, and Segmented-Price. For profit maximization, we design an algorithm using Two-Price Mechanisms that achieves $O(n^2 \log\log T)$ regret, where $n$ is the number of traders. For GFT maximization, the optimal regret depends critically on both market size and mechanism expressiveness. Constant regret is achievable in bilateral trade, but this guarantee breaks down as the market grows: even in a one-seller, two-buyer market, any algorithm using Single-Price Mechanisms suffers regret at least $Ω\!\big(\frac{\log\log T}{\log\log\log\log T}\big)$, and we provide a nearly matching $O(\log\log T)$ upper bound for general one-to-many markets. In full many-to-many markets, we prove that Two-Price Mechanisms inevitably incur linear regret $Ω(T)$ due to a \emph{mismatch phenomenon}, wherein inefficient pairings prevent near-optimal trade. To overcome this barrier, we introduce \emph{Segmented-Price Mechanisms}, which partition traders into groups and assign distinct prices per group. Using this richer mechanism, we design an algorithm achieving $O(n^2 \log\log T + n^3)$ regret for GFT maximization. Finally, we extend our results to the contextual setting, where traders' costs and values depend linearly on observed $d$-dimensional features that vary across rounds, obtaining regret bounds of $O(n^2 d \log\log T + n^2 d \log d)$ for profit and $O(n^2 d^2 \log T)$ for GFT. Our work delineates sharp boundaries between learnable and unlearnable regimes in two-sided dynamic pricing and demonstrates how modest increases in pricing expressiveness can circumvent fundamental hardness barriers.

cs.GT↗

arXiv2026

Contracting with a Mechanism Designer

This paper explores the economic interactions within modern crowdsourcing markets. In these markets, employers issue requests for tasks, platforms facilitate the recruitment of crowd workers, and workers complete tasks for monetary rewards. Recognizing that these roles serve distinct functions within the ecosystem, we introduce a three-party model that distinguishes among the principal (the requester), the intermediary (the platform), and the pool of agents (the workers). The principal, unable to directly engage with agents, relies on the intermediary to recruit and incentivize them. This interaction unfolds in two stages: first, the principal designs a profit-sharing contract with the intermediary; second, the intermediary implements a mechanism to select an agent to complete the delegated task. We analyze the proposed model as an extensive-form Stackelberg game. Our contributions are threefold. First, we fully characterize the subgame perfect equilibrium of our model. In particular, the principal's contract design problem can be represented as virtual value pricing, a novel auction-theoretic formulation. We identify the optimality of linear contracts, even when the task has multiple outcomes and agents' cost distributions are asymmetric. Second, to quantify the principal's utility loss from delegation and information asymmetry, we introduce the price of double marginalization (PoDM) and the classical price of anarchy (PoA). We derive tight or nearly tight bounds on both ratios under regular and monotone hazard rate distributions. Finally, we extend our analysis to two natural variants of the base model: (i) the intermediary is restricted to anonymous pricing mechanisms, and (ii) the principal lacks precise information about the market size.

cs.GT↗

arXiv2025

Contextual Search in Principal-Agent Games: The Curse of Degeneracy

In this work, we introduce and study contextual search in general principal-agent games, where a principal repeatedly interacts with agents by offering contracts based on contextual information and historical feedback, without knowing the agents' true costs or rewards. Our model generalizes classical contextual pricing by accommodating richer agent action spaces. Over $T$ rounds with $d$-dimensional contexts, we establish an asymptotically tight exponential $T^{1 - Θ(1/d)}$ bound in terms of the pessimistic Stackelberg regret, benchmarked against the best utility for the principal that is consistent with the observed feedback. We also establish a lower bound of $Ω(T^{\frac{1}{2}-\frac{1}{2d}})$ on the classic Stackelberg regret for principal-agent games, demonstrating a surprising double-exponential hardness separation from the contextual pricing problem (a.k.a, the principal-agent game with two actions), which is known to admit a near-optimal $O(d\log\log T)$ regret bound [Kleinberg and Leighton, 2003, Leme and Schneider, 2018, Liu et al., 2021]. In particular, this double-exponential hardness separation occurs even in the special case with three actions and two-dimensional context. We identify that this significant increase in learning difficulty arises from a structural phenomenon that we call contextual action degeneracy, where adversarially chosen contexts can make some actions strictly dominated (and hence unincentivizable), blocking the principal's ability to explore or learn about them, and fundamentally limiting learning progress.

cs.GT↗

arXiv2024

Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model

The facility location game has been studied extensively in mechanism design. In the classical model, each agent's cost is solely determined by her distance to the nearest facility. In this paper, we introduce a novel model where each facility charges an entrance fee. Thus, the cost of each agent is determined by both the distance to the facility and the entrance fee of the facility. In our model, the entrance fee function is allowed to be an arbitrary function, causing agents' preferences may no longer be single-peaked anymore: This departure from the classical model introduces additional challenges. We systematically delve into the intricacies of the model, designing strategyproof mechanisms with favorable approximation ratios. Additionally, we complement these ratios with nearly-tight impossibility results. Specifically, for one-facility and two-facility games, we provide upper and lower bounds for the approximation ratios given by deterministic and randomized mechanisms with respect to utilitarian and egalitarian objectives.

cs.GT↗

arXiv2024

Facility Assignment with Fair Cost Sharing: Equilibrium and Mechanism Design

In the one-dimensional facility assignment problem, m facilities and n agents are positioned along the real line. Each agent will be assigned to a single facility to receive service. Each facility incurs a building cost, which is shared equally among the agents utilizing it. Additionally, each agent independently bears a connection cost to access a facility. Thus, an agent's cost is the sum of the connection cost and her portion of the building cost. The social cost is the total cost of all agents. Notably, the optimal assignment that minimizes the social cost can be found in polynomial time. In this paper, we study the problem from two game-theoretical settings regarding the strategy space of agents and the rule the assignment. In both settings, agents act strategically to minimize their individual costs. In our first setting, the strategy space of agents is the set of facilities, granting agents the freedom to select any facility. Consequently, the self-formed assignment can exhibit instability, as agents may deviate to other facilities. We focus on the computation of an equilibrium assignment, where no agent has an incentive to unilaterally change her choice. We show that we can compute a pure Nash equilibrium in polynomial time. In our second setting, agents report their positions to a mechanism for assignment to facilities. The strategy space of agents becomes the set of all positions. Our interest lies in strategyproof mechanisms. It is essential to note that the preference induced by the agents' cost function is more complex as it depends on how other agents are assigned. We establish a strong lower bound against all strategyproof and anonymous mechanisms: none can achieve a bounded social cost approximation ratio. Nonetheless, we identify a class of non-trivial strategyproof mechanisms for any n and m that is unanimous and anonymous.

cs.GT↗