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Knapsack Auctions
 Proceedings of the Seventeenth Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... We consider a game theoretic knapsack problem that has application to auctions for selling advertisements on Internet search engines. Consider n agents each wishing to place an object in the knapsack. Each agent has a private valuation for having their object in the knapsack and each object has a pu ..."
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We consider a game theoretic knapsack problem that has application to auctions for selling advertisements on Internet search engines. Consider n agents each wishing to place an object in the knapsack. Each agent has a private valuation for having their object in the knapsack and each object has a publicly known size. For this setting, we consider the design of auctions in which agents have an incentive to truthfully reveal their private valuations. Following the framework of Goldberg et al. [10], we look to design an auction that obtains a constant fraction of the profit obtainable by a natural optimal pricing algorithm that knows the agents ’ valuations and object sizes. We give an auction that obtains a constant factor approximation in the nontrivial special case where the knapsack has unlimited capacity. We then reduce the limited capacity version of the problem to the unlimited capacity version via an approximately efficient auction (i.e., one that maximizes the social welfare). This reduction follows from generalizable principles. 1
Using Nash Implementation to Achieve Better Frugality Ratios
"... Abstract. Most of the recent works on algorithmic mechanism design exploit the solution concept of dominant strategy equilibria. Such work designs a proper payment scheme so that selfish agents maximize their utility by truthfully revealing their types. It has been pointed out that these truthful me ..."
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Abstract. Most of the recent works on algorithmic mechanism design exploit the solution concept of dominant strategy equilibria. Such work designs a proper payment scheme so that selfish agents maximize their utility by truthfully revealing their types. It has been pointed out that these truthful mechanisms, the famous among them being the VCG mechanisms, often incur high payments and fruglity ratios. In this work, we exploit the solution concept of Nash implementation to overcome this problem. Our mechanisms induce a set of Nash equilibria so that selfish agents have incentive to act based on a Nash equilibrium. We prove that our mechanisms enjoy substantial advantages over the truthful mechanisms in terms of payment and frugality. 1
Incentives in Large Random TwoSided Markets
, 2008
"... Many centralized twosided markets form a matching between participants by running a stable matching algorithm. It is a wellknown fact that no matching mechanism based on a stable matching algorithm can guarantee truthfulness as a dominant strategy for participants. However, we show that in a proba ..."
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Many centralized twosided markets form a matching between participants by running a stable matching algorithm. It is a wellknown fact that no matching mechanism based on a stable matching algorithm can guarantee truthfulness as a dominant strategy for participants. However, we show that in a probabilistic setting where the preference lists on one side of the market are composed of only a constant (independent of the size of the market) number of entries, each drawn from an arbitrary distribution, the number of participants that have more than one stable partner is vanishingly small. This proves (and generalizes) a conjecture of Roth and Peranson [42]. As a corollary of this result, we show that, with high probability, the truthful strategy is the best response for a random player when the other players are truthful. We also analyze equilibria of the deferred acceptance stable matching game. We show that the game with complete information has an equilibrium in which, in expectation, a (1 − o(1)) fraction of the strategies are truthful. In the more realistic setting of a game of incomplete information, we will show that the set of truthful stratiegs form a (1 + o(1))approximate BayesianNash equilibrium for uniformly random preferences. Our results have implications in many practical settings and were inspired by the work of Roth and Peranson [42] on the National Residency Matching Program.