We analyze the price of anarchy (POA) in a simple and practical non-truthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate second-price auctions. We first prove that under a standard "no overbidding" assumption, for every subadditive valuation profile, every pure Nash equilibrium has welfare at least 50% of optimal -i.e., the POA is at most 2. For the incomplete information setting, we prove that the POA with respect to BayesNash equilibria is strictly larger than 2 -an unusual separation from the full-information model -and is at most 2 ln m, where m is the number of goods.

Abstract. We consider a model of user engagement in social networks, where each player incurs a cost to remain engaged but derives a benefit proportional to the number of engaged neighbors. The natural equilibrium of this model corresponds to the k-core of the social network -the maximal induced subgraph with minimum degree at least k. We study the problem of "anchoring" a small number of vertices to maximize the size of the corresponding anchored k-core -the maximal induced subgraph in which every non-anchored vertex has degree at least k. This problem corresponds to preventing "unraveling" -a cascade of iterated withdrawals. We provide polynomialtime algorithms for general graphs with k = 2, and for boundedtreewidth graphs with arbitrary k. We prove strong inapproximability results for general graphs and k ≥ 3.

No abstract

No abstract

Modern ad auctions allow advertisers to target more specific segments of the user population. Unfortunately, this is not always in the best interest of the ad platform -partially hiding some information could be more beneficial for the platform's revenue. In this paper, we examine the following basic question in the context of second-price ad auctions: how should an ad platform optimally reveal information about the ad opportunity to the advertisers in order to maximize revenue? We consider a model in which bidders' valuations depend on a random state of the ad opportunity. Different from previous work, we focus on a more practical, and challenging, situation where the space of possible realizations of ad opportunities is extremely large. We thus focus on developing algorithms whose running time is polynomial in the number of bidders, but is independent of the number of ad opportunity realizations.We assume that the auctioneer can commit to a signaling scheme to reveal noisy information about the realized state of the ad opportunity, and examine the auctioneer's algorithmic question of designing the optimal signaling scheme. We first consider that the auctioneer is restricted to send a public signal to all bidders. As a warm-up, we start with a basic (though less realistic) setting in which the auctioneer knows the bidders' valuations, and show that an -optimal scheme can be implemented in time polynomial in the number of bidders and 1/ . We then move to a wellmotivated Bayesian valuation setting in which the auctioneer and bidders both have private information, and present two results. First, we exhibit a characterization result regarding approximately optimal schemes and prove that any constantapproximate public signaling scheme must use exponentially many signals. Second, we present a "simple" public signaling scheme that serves as a constant approximation under mild assumptions.Finally, we initiate an exploration on the power of being able to send different signals privately to different bidders. In the basic setting where the auctioneer knows bidders' valuations, we exhibit a polynomial-time private scheme that extracts almost full surplus even in the worst Bayes Nash equilibrium. This illustrates the surprising power of private signaling schemes in extracting revenue.