Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Competitive generalized auctions
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Reducing mechanism design to algorithm design via machine learning
Journal of Computer and System Sciences
Multi-unit Auctions with Budget Limits
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the 12th ACM conference on Electronic commerce
Mechanism design via consensus estimates, cross checking, and profit extraction
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Polyhedral clinching auctions and the adwords polytope
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Prior-free auctions with ordered bidders
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Mechanism Design via Consensus Estimates, Cross Checking, and Profit Extraction
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
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We consider prior-free auctions for revenue and welfare maximization when agents have a common budget. The abstract environments we consider are ones where there is a downward-closed and symmetric feasibility constraint on the probabilities of service of the agents. These environments include position auctions where slots with decreasing click-through rates are auctioned to advertisers. We generalize and characterize the envy-free benchmark from Hartline and Yan [2011] to settings with budgets and characterize the optimal envy-free outcomes for both welfare and revenue. We give prior-free mechanisms that approximate these benchmarks. A building block in our mechanism is a clinching auction for position auction environments. This auction is a generalization of the multi-unit clinching auction of Dobzinski et al. [2008] and a special case of the polyhedral clinching auction of Goel et al. [2012]. For welfare maximization, we show that this clinching auction is a good approximation to the envy-free optimal welfare for position auction environments. For profit maximization, we generalize the random sampling profit extraction auction from Fiat et al. [2002] for digital goods to give a 10.0-approximation to the envy-free optimal revenue in symmetric, downward-closed environments. Even without budgets this revenue maximization question is of interest and we obtain an improved approximation bound of 7.5 (from 30.4 by Ha and Hartline [2012]).