arXiv subjects

Edwin Lock

Publications and source records attributed to Edwin Lock.

13 recordsLinked to original sources

arXiv2026

Efficiently Restructuring Sovereign Debt via Arctic Auctions with Convex Costs

We study the problem of computing competitive equilibria in the Arctic product-mix auction, originally developed for the Icelandic government for exchanging blocked financial accounts, and more recently proposed by IMF staff for sovereign debt restructuring. From the buyers' perspective, the Arctic auction is equivalent to the quasi-linear Fisher market. However, unlike the standard Fisher model, the seller can express rich supply preferences through explicit supply-side costs and constraints. Despite extensive algorithmic literature on Fisher markets, the seller side has not received much attention, and no polynomial-time algorithm was previously known for computing competitive equilibrium when sellers face nontrivial costs. We examine the natural and expressive regime of separable, stepwise-increasing marginal costs that underlie the above-stated applications. Using polyhedral theory techniques, we first show that rational inputs lead to rational-valued competitive equilibria. Motivated by this result, we develop the first polynomial-time algorithm for this setting based on a non-trivial extension of classic primal-dual balanced-flow techniques for linear Fisher markets. Our work provides a robust computational foundation for auctions with sophisticated preferences, paving the way for flexible and institutionally feasible market designs in global finance.

cs.GT↗

arXiv2026

Decentralized Trading Networks: Equilibria and Fairness

We explore stability and fairness considerations in decentralized networked markets with bilateral contracts, building on the trading networks framework [Hatfield et al., 2013]. In our trading network game, we show that a well-defined subset of Nash equilibria can be supported as competitive equilibria. Considering an offer-based trading dynamic as well as a stochastic price clock market, we prove new convergence results to Nash equilibrium and competitive equilibrium, providing a rationale for stability properties in decentralized, dynamic trading networks. Turning to the tension between fairness and (core) stability, we prove several negative results: inessential agents always receive zero utility in any core outcome, and even essential agents can get zero utility in all core outcomes.

econ.TH↗

arXiv2026

The Computational Intractability of Not Worst Responding

Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement that each player merely avoid worst responses -- arguably the weakest meaningful rationality criterion -- yields tractable solution concepts. We show that it does not: any solution concept with this minimal guarantee is ``as intractable'' as pure Nash equilibrium. In general games, determining the existence of no-worst-response action profiles is NP-complete, finding one is NP-hard, and counting them is #P-complete. In potential games, where existence is guaranteed, the search problem is PLS-complete. Computational intractability therefore stems not only from the requirement of optimality, but also from the requirement of a minimal rationality guarantee for each player. Moreover, relaxing the latter requirement gives rise to a tractability trade-off between the strength of individual rationality guarantees and the fraction of players satisfying them.

cs.GT↗

arXiv2025

Accelerated Preference Elicitation with LLM-Based Proxies

Bidders in combinatorial auctions face significant challenges when describing their preferences to an auctioneer. Classical work on preference elicitation focuses on query-based techniques inspired from proper learning--often via proxies that interface between bidders and an auction mechanism--to incrementally learn bidder preferences as needed to compute efficient allocations. Although such elicitation mechanisms enjoy theoretical query efficiency, the amount of communication required may still be too cognitively taxing in practice. We propose a family of efficient LLM-based proxy designs for eliciting preferences from bidders using natural language. Our proposed mechanism combines LLM pipelines and DNF-proper-learning techniques to quickly approximate preferences when communication is limited. To validate our approach, we create a testing sandbox for elicitation mechanisms that communicate in natural language. In our experiments, our most promising LLM proxy design reaches approximately efficient outcomes with five times fewer queries than classical proper learning based elicitation mechanisms.

cs.GT↗

arXiv2024

Decentralized Convergence to Equilibrium Prices in Trading Networks

We propose a decentralized market model in which agents can negotiate bilateral contracts. This builds on a similar, but centralized, model of trading networks introduced by Hatfield et al. in 2013. Prior work has established that fully-substitutable preferences guarantee the existence of competitive equilibria which can be centrally computed. Our motivation comes from the fact that prices in markets such as over-the-counter markets and used car markets arise from decentralized negotiation among agents, which has left open an important question as to whether equilibrium prices can emerge from agent-to-agent bilateral negotiations. We design a best response dynamic intended to capture such negotiations between market participants. We assume fully substitutable preferences for market participants. In this setting, we provide proofs of convergence for sparse markets (covering many real world markets of interest), and experimental results for more general cases, demonstrating that prices indeed reach equilibrium, quickly, via bilateral negotiations. Our best response dynamic, and its convergence behavior, forms an important first step in understanding how decentralized markets reach, and retain, equilibrium.

cs.GT↗

arXiv2024

The Computational Complexity of the Housing Market

We prove that the classic problem of finding a competitive equilibrium in an exchange economy with indivisible goods, money, and unit-demand agents is PPAD-complete. In this "housing market", agents have preferences over the house and amount of money they end up with, but can experience income effects. Our results contrast with the existence of polynomial-time algorithms for related problems: Top Trading Cycles for the "housing exchange" problem in which there are no transfers and the Hungarian algorithm for the "housing assignment" problem in which agents' utilities are linear in money. Along the way, we prove that the Rainbow-KKM problem, a total search problem based on a generalization by Gale of the Knaster-Kuratowski-Mazurkiewicz lemma, is PPAD-complete. Our reductions also imply bounds on the query complexity of finding competitive equilibrium.

cs.GT↗

arXiv2023

Competitive and Revenue-Optimal Pricing with Budgets

In markets with budget-constrained buyers, competitive equilibria need not be efficient in the utilitarian sense, or maximise the seller's revenue. We consider a setting with multiple divisible goods. Competitive equilibrium outcomes, and only those, are constrained utilitarian efficient, a notion of utilitarian efficiency that respects buyers' demands and budgets. Our main contribution establishes that, when buyers have linear valuations, competitive equilibrium prices are unique and revenue-optimal for a zero-cost seller.

econ.TH↗

arXiv2023

Optimal Testing and Containment Strategies for Universities in Mexico amid COVID-19

This work sets out a testing and containment framework developed for reopening universities in Mexico following the lockdown due to COVID-19. We treat diagnostic testing as a resource allocation problem and develop a testing allocation mechanism and practical web application to assist educational institutions in making the most of limited testing resources. In addition to the technical results and tools, we also provide a reflection on our current experience of running a pilot of our framework within the Instituto Tecnol\'ogico y de Estudios Superiores de Monterrey (ITESM), a leading private university in Mexico, as well as on our broader experience bridging research with academic policy in the Mexican context.

cs.GT↗

arXiv2022

Welfare-Maximizing Pooled Testing

Pooled testing increases the reach of scarce diagnostic resources, but optimally composing pools for individuals differing in infection risk and the utility they derive from a negative test is combinatorially challenging. We study the problem of maximizing the expected welfare of individuals cleared by a negative result, given a testing budget. Assigning a sample to several pools can raise welfare but is operationally burdensome; we show the restriction to non-overlapping allocations costs at most a factor of two for any budget or population, less under a pool-size cap at high health probabilities, and nothing when no health probability exceeds one-half. Welfare decomposes across non-overlapping pools, whereas evaluating overlapping allocations is #P-hard for pools of three or more. Finding optimal allocations is NP-hard and admits no FPTAS, with or without overlap, unless P = NP. We provide single-test routines and greedy algorithms with constant-factor guarantees. On real-world data, greedy achieves over 99% of optimal non-overlapping welfare in milliseconds, against hours for exact benchmarks. In a randomized field experiment at a Mexican research institute, our mechanism conditioned campus access on negative qPCR results. Relative to unrestricted access, we found no statistical evidence of adverse effects on participants' performance, learning, or mental health.

cs.GT↗

arXiv2020

Learning Strong Substitutes Demand via Queries

This paper addresses the computational challenges of learning strong substitutes demand when given access to a demand (or valuation) oracle. Strong substitutes demand generalises the well-studied gross substitutes demand to a multi-unit setting. Recent work by Baldwin and Klemperer shows that any such demand can be expressed in a natural way as a finite list of weighted bid vectors. A simplified version of this bidding language has been used by the Bank of England. Assuming access to a demand oracle, we provide an algorithm that computes the unique list of weighted bid vectors corresponding to a bidder's demand preferences. In the special case where their demand can be expressed using positive bids only, we have an efficient algorithm that learns this list in linear time. We also show super-polynomial lower bounds on the query complexity of computing the list of bids in the general case where bids may be positive and negative. Our algorithms constitute the first systematic approach for bidders to construct a bid list corresponding to non-trivial demand, allowing them to participate in `product-mix' auctions.

cs.GT↗

arXiv2020

Maximising the Benefits of an Acutely Limited Number of COVID-19 Tests

We propose a novel testing and containment strategy in order to contain the spread of SARS-CoV2 while permitting large parts of the population to resume social and economic activity. Our approach recognises the fact that testing capacities are severely constrained in many countries. In this setting, we show that finding the best way to utilise this limited number of tests during a pandemic can be formulated concisely as an allocation problem. Our problem formulation takes into account the heterogeneity of the population and uses pooled testing to identify and isolate individuals while prioritising key workers and individuals with a higher risk of spreading the disease. In order to demonstrate the efficacy of our testing and containment mechanism, we perform simulations using a network-based SIR model. Our simulations indicate that applying our mechanism on a population of $100,000$ individuals with only $16$ tests per day reduces the peak number of infected individuals by approximately $20\%$, when compared to the scenario where no intervention is implemented.

q-bio.PE↗

arXiv2019

Solving Strong-Substitutes Product-Mix Auctions

This paper develops algorithms to solve strong-substitutes product-mix auctions. That is, it finds competitive equilibrium prices and quantities for agents who use this auction's bidding language to truthfully express their strong-substitutes preferences over an arbitrary number of goods, each of which is available in multiple discrete units. (Strong substitutes preferences are also known, in other literatures, as $M^\natural$-concave, matroidal and well-layered maps, and valuated matroids). Our use of the bidding language, and the information it provides, contrasts with existing algorithms that rely on access to a valuation or demand oracle to find equilibrium. We compute market-clearing prices using algorithms that apply existing submodular minimisation methods. Allocating the supply among the bidders at these prices then requires solving a novel constrained matching problem. Our algorithm iteratively simplifies the allocation problem, perturbing bids and prices in a way that resolves tie-breaking choices created by bids that can be accepted on more than one good. We provide practical running time bounds on both price-finding and allocation, and illustrate experimentally that our allocation mechanism is practical.

cs.GT↗

arXiv2018

Characterising and recognising game-perfect graphs

Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once the graph is fully coloured, in which case the maker wins, or the graph can no longer be fully coloured, in which case the breaker wins. In the game $g_B$, the breaker makes the first move. Our main focus is on the class of $g_B$-perfect graphs: graphs such that for every induced subgraph $H$, the game $g_B$ played on $H$ admits a winning strategy for the maker with only $\omega(H)$ colours, where $\omega(H)$ denotes the clique number of $H$. Complementing analogous results for other variations of the game, we characterise $g_B$-perfect graphs in two ways, by forbidden induced subgraphs and by explicit structural descriptions. We also present a clique module decomposition, which may be of independent interest, that allows us to efficiently recognise $g_B$-perfect graphs.

math.CO↗