Envy-free auctions for digital goods
Proceedings of the 4th ACM conference on Electronic commerce
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Multi-unit auctions with budget-constrained bidders
Proceedings of the 6th ACM conference on Electronic commerce
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal envy-free pricing with metric substitutability
Proceedings of the 9th ACM conference on Electronic commerce
Multi-unit Auctions with Budget Limits
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
General auction mechanism for search advertising
Proceedings of the 18th international conference on World wide web
On the importance of migration for fairness in online grid markets
GRID '08 Proceedings of the 2008 9th IEEE/ACM International Conference on Grid Computing
Envy-free makespan approximation: extended abstract
Proceedings of the 11th ACM conference on Electronic commerce
An expressive mechanism for auctions on the web
Proceedings of the 20th international conference on World wide web
A global characterization of envy-free truthful scheduling of two tasks
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Revenue maximizing envy-free multi-unit auctions with budgets
Proceedings of the 13th ACM Conference on Electronic Commerce
Envy-Free Makespan Approximation
SIAM Journal on Computing
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We study the problem of identifying prices to support a given allocation of items to bidders in an envy-free way. A bidder will envy another bidder if she would prefer to obtain the other bidder's item at the price paid by that bidder. Envy-free prices for allocations have been studied extensively; here, we focus on the impact of budgets: beyond their willingness to pay for items, bidders are also constrained by their ability to pay, which may be lower than their willingness.In a recent paper, Aggarwal et al. show that a variant of the Ascending Auction finds a feasible and bidder-optimal assignment and supporting envy-free prices in polynomial time so long as the input satisfies certain non-degeneracy conditions. While this settles the problem of finding a feasible allocation, an auctioneer might sometimes also be interested in a specific allocation of items to bidders. We present two polynomial-time algorithms for this problem, one which finds maximal prices supporting the given allocation (if such prices exist), and another which finds minimal prices. We also prove a structural result characterizing when different allocations are supported by the same minimal price vector.