School of C o m p u t e r Science a n d Engineering, H e b r e w University, J e r u s a l e m 91904, Israel A b s t r a c t This paper deals with multi-unit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both on-line and off-line scenarios. This is the first result where non-VCG mechanisms are derived for non-single minded bidders for a natural model of combinatorial auctions.

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by traders. Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market Preliminary versions of some of the results in this paper were presented in two conference papers, Chen et al. [10] and Dimitrov and Sami [13]. Algorithmica (2010) 58: 930-969 931scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for the infinite-stage market with discounting, the market price converges to the fully-revealing price, and the rate of convergence can be bounded in terms of the discounting parameter. When signals are conditionally independent, truthful betting is the unique WPBE for the infinite-stage market with and without discounting.

Finding optimal solutions for multi-unit combinatorial auctions is a hard problem and finding approximations to the optimal solution is also hard. We investigate the use of Branch-and-Bound techniques: they require both a way to bound from above the value of the best allocation and a good criterion to decide which bids are to be tried first. Different methods for efficiently bounding from above the value of the best allocation are considered. Theoretical original results characterize the best approximation ratio and the ordering criterion that provides it. We suggest to use this criterion.

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We study k-resilient Nash equilibria, joint strategies where no member of a coalition C of size up to k can do better, even if the whole coalition defects. We show that such k-resilient Nash equilibria exist for secret sharing and multiparty computation, provided that players prefer to get the information than not to get it. Our results hold even if there are only 2 players, so we can do multiparty computation with only two rational agents. We extend our results so that they hold even in the presence of up to t players with "unexpected" utilities. Finally, we show that our techniques can be used to simulate games with mediators by games without mediators.

School of C o m p u t e r Science a n d Engineering, H e b r e w University, J e r u s a l e m 91904, Israel A b s t r a c t This paper deals with multi-unit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both on-line and off-line scenarios. This is the first result where non-VCG mechanisms are derived for non-single minded bidders for a natural model of combinatorial auctions.

We study the effects of campaigning, where the society is partitioned into voter clusters and a diffusion process propagates opinions in a network connecting those clusters. Our model is very general and can incorporate many campaigning actions, various partitions of the society into voter clusters, and very general diffusion processes. Perhaps surprisingly, we show that computing the cheapest campaign for rigging a given election can usually be done efficiently, even with arbitrarily-many voters.

This paper presents a truthful sponsored search auction based on an incentive-compatible multi-armed bandit mechanism. The mechanism described combines several desirable traits. The mechanism gives advertisers the incentive to report their true bid, learns the click-through rate for advertisements, allows for slots with different quality, and loses the minimum welfare during the sampling process.The underlying generalization of the multi-armed bandit mechanism addresses the interplay between exploration and exploitation in an online setting that is truthful in high probability while allowing for slots of different quality. As the mechanism progresses the algorithm more closely approximates the hidden variables (clickthough rates) in order to allocate advertising slots to the best advertisements. The resulting mechanism obtains the optimal welfare apart from a tightly bounded loss of welfare caused by the bandit sampling process.Of independent interest, in the field of economics it has long been recognized that preference elicitation is difficult to achieve, mainly as people are unaware of how much happiness a particular good will bring to them. In this paper we alleviate this problem somewhat by introducing a valuation-discovery process to the mechanism which results in a preference-elicitation mechanism for advertisers and search engines.