Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.30702

From Bilateral Trade to Matching Markets: Sharp Gains from Trade

Zhengyang Liu·Ying Qin·Zihe Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study gains from trade in matching markets with independent private values and costs, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. A second-best guarantee for finite bilateral trade extends without loss to matching markets with independent Borel priors, arbitrary downward-closed feasibility, and finite expected first-best gains. For bounded buyers with monotone hazard rates and arbitrary bounded sellers, we determine the exact worst-case ratio of second-best to first-best gains, approximately $0.72490721$. For binary buyers and sellers with at most $m$ types, we determine the exact ratio for every $m$, including $8/9$ when $m=2$ and a limit of $4/5$ as $m$ grows. Both families of bounds are tight already in bilateral trade.

Explore related subjects

cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zhengyang Liu, Ying Qin, Zihe Wang. 2026-09-25. From Bilateral Trade to Matching Markets: Sharp Gains from Trade. https://arxiv.org/abs/2609.30702

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Dynamic Welfare-Maximizing Pooled Testing

Pooled testing uses one test to certify several agents as healthy when the pooled result is negative. We study a budget-constrained welfare problem in which agents have heterogeneous utilities and independent prior probabilities of being healthy. Welfare is earned when an agent is certified healthy, and a dynamic policy may choose each pool after observing earlier test outcomes. We ask how much such adaptation can improve over a static allocation that fixes all pools in advance. Our main result proves that the optimal dynamic policy has value at most twice that of the optimal static overlapping allocation, for every population, test budget, and pool-size cap. The proof samples a path through the dynamic policy using an independent health profile, randomly thins the selected pools, and compares the resulting static allocation with the dynamic policy one agent at a time. A Boolean-cube argument proves the comparison on uniform subcubes, and a complementary-profile coupling lifts the result to arbitrary heterogeneous product priors. We also identify regimes in which adaptivity has no value, show that strict adaptive gains require re-pooling agents after positive tests, and give a three-agent instance in which adaptation is strictly beneficial. Exact-Joint Greedy obtains a $1/(e+1)$ fraction of optimal static overlapping welfare. The static non-overlapping Greedy algorithm of Finster et al. has the same guarantee, hence our factor-two theorem newly implies that each is a $2(e+1)$-approximation to the optimal dynamic policy. Finally, a reproducible exact small-instance study compares the dynamic and static benchmarks and greedy policies. The appendix records separate exploratory results for Gibbs-marginal and reinforcement-learning approaches at larger scales.

cs.GT↗
arXiv2026

Induced Representations in Cooperative Games with Homogeneous Groups of Players

Oftentimes, the Shapley value, a measure of the contribution of a player to a game, becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of a homogeneous group game by using an induced representation from a Young subgroup. We prove that the depth of interaction of a two-group game is limited by the size of the minority group. Therefore, the algebraic structure of the game filters out a large space of irrelevant complexities. We then show that this filtration constrains any symmetric linear value to a specific subspace. This recovers the Shapley value uniquely for games consisting of exactly two homogeneous groups under standard axioms. Finally, we explore applications to the UN Security Council and complementary goods markets to illustrate the practical power of this approach.

cs.GT↗
arXiv2026

Endogenous Information in Routing Games: Memory-Constrained Equilibria, Recall Braess Paradoxes, and Memory Design

We study routing games in which travelers optimize over routes that are remembered or surfaced, rather than over a fixed exogenous action set. The paper develops a tractable design theory for endogenous recall and then connects it back to an explicit finite-memory micro model. At the micro level, each traveler carries a finite memory state, receives surfaced alternatives, chooses via a logit rule, and updates memory under a policy such as LRU. This yields a stationary Forgetful Wardrop Equilibrium (FWE); existence is proved under mild regularity, and uniqueness follows in a contraction regime for the reduced fixed-point map. The paper's main design layer is a stationary salience model that summarizes persistent memory and interface effects as route-specific weights. Salience-weighted stochastic user equilibrium is the unique minimizer of a strictly convex potential, which yields a clean optimization and implementability theory. In this layer we characterize governed implementability under ratio budgets and affine tying constraints, and derive constructive algorithms on parallel and series-parallel networks. The bridge between layers is exact for last-choice memory (B=1): the micro model is then equivalent to the salience model, so any interior salience vector can be realized by an appropriate surfacing policy. For larger memories, we develop an explicit LRU-to-TTL-to-salience approximation pipeline and add contraction-based bounds that translate surrogate-map error into fixed-point and welfare error. Finally, we define a Recall Braess Paradox, in which improving recall increases equilibrium delay without changing physical capacity, and show that it can arise on every two-terminal network with at least two distinct s-t paths. Targeted experiments support the approximation regime, governed-design predictions, and the computational advantages of the reduced layer.

cs.GT↗