A further note on the stable matching problem
Discrete Applied Mathematics
The complexity of theorem-proving procedures
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Multi-unit auctions with budget-constrained bidders
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Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
AdWords and generalized online matching
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Algorithmic Game Theory
The computation of approximate competitive equilibrium is PPAD-hard
Information Processing Letters
Multi-unit Auctions with Budget Limits
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Hybrid keyword search auctions
Proceedings of the 18th international conference on World wide web
General auction mechanism for search advertising
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A theory of expressiveness in mechanisms
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Methodology for designing reasonably expressive mechanisms with application to ad auctions
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Envy-Free Allocations for Budgeted Bidders
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Bidder Optimal Assignments for General Utilities
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Expressive auctions for externalities in online advertising
Proceedings of the 19th international conference on World wide web
Competitive equilibria in matching markets with budgets
ACM SIGecom Exchanges
Sponsored search auctions with conflict constraints
Proceedings of the fifth ACM international conference on Web search and data mining
On multiple keyword sponsored search auctions with budgets
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Co-evolution-based mechanism design for sponsored search advertising
Electronic Commerce Research and Applications
Sponsored search, market equilibria, and the Hungarian Method
Information Processing Letters
Bidder optimal assignments for general utilities
Theoretical Computer Science
Optimal auctions via the multiplicative weight method
Proceedings of the fourteenth ACM conference on Electronic commerce
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Auctions are widely used on the Web. Applications range from internet advertising to platforms such as eBay. In most of these applications the auctions in use are single/multi-item auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is the limited expressiveness that they offer to the bidders. The General Auction Mechanism (GAM) of [1] is taking a first step towards addressing the problem of limited expressiveness by computing a bidder optimal, envy free outcome for linear utility functions with identical slopes and a single discontinuity per bidder-item pair. We show that in many practical situations this does not suffice to adequately model the preferences of the bidders, and we overcome this problem by presenting the first mechanism for piece-wise linear utility functions with non-identical slopes and multiple discontinuities. Our mechanism runs in polynomial time. Like GAM it is incentive compatible for inputs that fulfill a certain non-degeneracy requirement, but our requirement is more general than the requirement of GAM. For discontinuous utility functions that are non-degenerate as well as for continuous utility functions the outcome of our mechanism is a competitive equilibrium. We also show how our mechanism can be used to compute approximately bidder optimal, envy free outcomes for a general class of continuous utility functions via piece-wise linear approximation. Finally, we prove hardness results for even more expressive settings.