arXiv subjects

Eric Yan

Publications and source records attributed to Eric Yan.

5 recordsLinked to original sources

arXiv2026

Pre-auction strategic communication

High-stakes auctions are often preceded by nonbinding communication between bidders and the seller. I study a two-period model in which bidders privately send cheap-talk messages to the seller about their valuations before the seller decides whether to run a mechanism or take a forfeitable outside option. The seller has commitment within the second-period mechanism but not over how she uses first-period communication. In monotone bidder-symmetric equilibria, an unrestricted seller runs at most one mechanism on the equilibrium path: a second-price auction with a common reserve, and only when all bidders report values above a common threshold. Thus discriminatory auctions cannot arise in equilibrium, despite asymmetric on-path posteriors. With two bidders, the seller is better off, and can sometimes attain her full-commitment payoff, if she can commit ex-ante to second-price auctions with a common reserve.

econ.TH↗

arXiv2024

Information About Other Players in Mechanism Design

We study mechanism design settings where the planner has an interest in agents receiving noisy signals about the types of other agents. We show that additional information about other agents can eliminate undesired equilibria, making it helpful to a planner interested in full implementation, designing a mechanism for which every equilibrium outcome is desirable. We provide a sufficient condition under which a social choice function that is not fully implementable when agents have no information about types of other agents can become fully implementable when agents have additional information.

econ.TH↗

arXiv2023

Universality for Cokernels of Dedekind Domain Valued Random Matrices

We use the moment method of Wood to study the distribution of random finite modules over a countable Dedekind domain with finite quotients, generated by taking cokernels of random $n\times n$ matrices with entries valued in the domain. Previously, Wood found that when the entries of a random $n\times n$ integral matrix are not too concentrated modulo a prime, the asymptotic distribution (as $n\to\infty$) of the cokernel matches the Cohen and Lenstra conjecture on the distribution of class groups of imaginary quadratic fields. We develop and prove a condition that produces a similar universality result for random matrices with entries valued in a countable Dedekind domain with finite quotients.

math.NT↗

arXiv2021

The Determinant of $\{\pm 1\}$-Matrices and Oriented Hypergraphs

The determinants of $\{\pm 1\}$-matrices are calculated by via the oriented hypergraphic Laplacian and summing over an incidence generalization of vertex cycle-covers. These cycle-covers are signed and partitioned into families based on their hyperedge containment. Every non-edge-monic family is shown to contribute a net value of $0$ to the Laplacian, while each edge-monic family is shown to sum to the absolute value of the determinant of the original incidence matrix. Simple symmetries are identified as well as their relationship to Hadamard's maximum determinant problem. Finally, the entries of the incidence matrix are reclaimed using only the signs of an adjacency-minimal set of cycle-covers from an edge-monic family.

math.CO↗

arXiv2020

Oriented Hypergraphs: Balanceability

An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance.

math.CO↗