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We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities.

Data Structures and Algorithms · Computer Science 2014-03-25 Ran Duan , Kurt Mehlhorn

We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…

Discrete Mathematics · Computer Science 2023-08-21 Nina Chiarelli , Matjaž Krnc , Martin Milanič , Ulrich Pferschy , Joachim Schauer

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…

Computer Science and Game Theory · Computer Science 2023-07-11 Elizabeth Baldwin , Paul W. Goldberg , Paul Klemperer , Edwin Lock

Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program…

Computer Science and Game Theory · Computer Science 2025-07-08 Sébastien Lahaie , Benjamin Lubin

This paper investigates the problem of proportionally fair double sided energy auction involving buying and selling agents. The grid is assumed to be operating under islanded mode. A distributed auction algorithm that can be implemented by…

Computer Science and Game Theory · Computer Science 2016-05-24 M. Nazif Faqiry , Sanjoy Das

We study the complexity of computing Bayes-Nash equilibria in single-item first-price auctions. We present the first efficient algorithms for the problem, when the bidders' values for the item are independently drawn from the same…

Computer Science and Game Theory · Computer Science 2026-03-26 Aris Filos-Ratsikas , Yiannis Giannakopoulos , Alexandros Hollender , Charalampos Kokkalis

In this article we consider combinatorial markets with valuations only for singletons and pairs of buy/sell-orders for swapping two items in equal quantity. We provide an algorithm that permits polynomial time market-clearing and -pricing.…

Optimization and Control · Mathematics 2017-10-30 Johannes C. Müller , Sebastian Pokutta , Alexander Martin , Susanne Pape , Andrea Peter , Thomas Winter

The problem of allocating scarce items to individuals is an important practical question in market design. An increasingly popular set of mechanisms for this task uses the concept of market equilibrium: individuals report their preferences,…

Computer Science and Game Theory · Computer Science 2019-12-11 Riley Murray , Christian Kroer , Alex Peysakhovich , Parikshit Shah

In a combinatorial exchange setting, players place sell (resp. buy) bids on combinations of traded goods. Besides the question of finding an optimal selection of winning bids, the question of how to share the obtained profit is of high…

Computer Science and Game Theory · Computer Science 2021-06-30 T. Heller , S. O. Krumke

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…

Theoretical Economics · Economics 2022-11-17 Moshe Babaioff , Nicole Immorlica , Yingkai Li , Brendan Lucier

We show that a competitive equilibrium always exists in combinatorial auctions with anonymous graphical valuations and pricing, using discrete geometry. This is an intuitive and easy-to-construct class of valuations that can model both…

Combinatorics · Mathematics 2021-11-08 Marie-Charlotte Brandenburg , Christian Haase , Ngoc Mai Tran

A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify robust natural distributed algorithms that converge quickly to an equilibrium.…

Computer Science and Game Theory · Computer Science 2019-11-25 Richard Cole , Yixin Tao

Revenue-optimal auction design is a challenging problem with significant theoretical and practical implications. Sequential auction mechanisms, known for their simplicity and strong strategyproofness guarantees, are often limited by…

Computer Science and Game Theory · Computer Science 2024-07-12 Sai Srivatsa Ravindranath , Zhe Feng , Di Wang , Manzil Zaheer , Aranyak Mehta , David C. Parkes

Matching problems have been widely studied in the research community, especially Ad-Auctions with many applications ranging from network design to advertising. Following the various advancements in machine learning, one natural question is…

Data Structures and Algorithms · Computer Science 2024-02-15 Eniko Kevi , Nguyen Kim Thang

Equilibrium computation in markets usually considers settings where player valuation functions are known. We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of…

Computer Science and Game Theory · Computer Science 2021-09-10 Vignesh Viswanathan , Omer Lev , Neel Patel , Yair Zick

In this work we consider selling items using a sequential first price auction mechanism. We generalize the assumption of conservative bidding to extensive form games (henceforth optimistic conservative bidding), and show that for both…

Computer Science and Game Theory · Computer Science 2015-02-02 Avinatan Hassidim , Yishay Mansour

Statistical inference under market equilibrium effects has attracted increasing attention recently. In this paper we focus on the specific case of linear Fisher markets. They have been widely use in fair resource allocation of food/blood…

Econometrics · Economics 2025-02-19 Luofeng Liao , Yuan Gao , Christian Kroer

We consider the problem of large-scale Fisher market equilibrium computation through scalable first-order optimization methods. It is well-known that market equilibria can be captured using structured convex programs such as the…

Computer Science and Game Theory · Computer Science 2023-03-02 Tianlong Nan , Yuan Gao , Christian Kroer

Combinatorial Auctions are a central problem in Algorithmic Mechanism Design: pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare, revenue, or profit). The…

Computer Science and Game Theory · Computer Science 2015-03-19 Avrim Blum , Anupam Gupta , Yishay Mansour , Ankit Sharma

We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both…

Computer Science and Game Theory · Computer Science 2012-04-20 Avital Gutman , Noam Nisan