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We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the "input size" is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2-approximation for the more restricted case of "XOS bidders", a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems.

In this letter we present a brief report of our recent research on information distribution mechanisms in networks [Babaioff et al. 2011]. We study scenarios in which all nodes that become aware of the information compete for the same prize, and thus have an incentive not to propagate information. Examples of such scenarios include the 2009 DARPA Network Challenge (finding red balloons), and raffles. We give special attention to one application domain, namely Bitcoin, a decentralized electronic currency system. We propose reward schemes that will remedy an incentives problem in Bitcoin in a Sybil-proof manner, with little payment overhead.

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