Very recently, Hartline and Lucier [14] studied singleparameter mechanism design problems in the Bayesian setting. They proposed a black-box reduction that converted Bayesian approximation algorithms into Bayesian-Incentive-Compatible (BIC) mechanisms while preserving social welfare. It remains a major open question if one can find similar reduction in the more important multi-parameter setting. In this paper, we give positive answer to this question when the prior distribution has finite and small support. We propose a black-box reduction for designing BIC multi-parameter mechanisms. The reduction converts any algorithm into an ɛ-BIC mechanism with only marginal loss in social welfare. As a result, for combinatorial auctions with sub-additive agents we get an ɛ-BIC mechanism that achieves constant approximation. 1

Abstract. Consider a random graph model where each possible edge e is present independently with some probability pe. We are given these numbers pe, and want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced to add it to our matching. Further, each vertex i is allowed to be queried at most ti times. How should we adaptively query the edges to maximize the expected weight of the matching? We consider several matching problems in this general framework (some of which arise in kidney exchanges and online dating, and others arise in modeling online advertisements); we give LP-rounding based constantfactor approximation algorithms for these problems. Our main results are: • We give a 5.75-approximation for weighted stochastic matching on general graphs, and a 5-approximation on bipartite graphs. This answers an open question from [Chen et al. ICALP 09]. • Combining our LP-rounding algorithm with the natural greedy algorithm, we give an improved 3.88-approximation for unweighted stochastic matching on general graphs and 3.51-approximation on bipartite graphs. • We introduce a generalization of the stochastic online matching problem [Feldman et al. FOCS 09] that also models preferenceuncertainty and timeouts of buyers, and give a constant factor approximation algorithm. 1

We design algorithms for computing approximately revenue-maximizing sequential postedpricing mechanisms (SPM) in K-unit auctions, in a standard Bayesian model. A seller has K copies of an item to sell, and there are n buyers, each interested in only one copy, who have some value for the item. The seller must post a price for each buyer, the buyers arrive in a sequence enforced by the seller, and a buyer buys the item if its value exceeds the price posted to it. The seller does not know the values of the buyers, but have Bayesian information about them. An SPM specifies the ordering of buyers and the posted prices, and may be adaptive or non-adaptive in its behavior. The goal is to design SPM in polynomial time to maximize expected revenue. We compare against the expected revenue of optimal SPM, and provide a polynomial time approximation scheme (PTAS) for both non-adaptive and adaptive SPMs. This is achieved by two algorithms: an efficient algorithm that gives a (1 − 1 √)-approximation (and hence a PTAS for sufficiently 2πK large K), and another that is a PTAS for constant K. The first algorithm yields a non-adaptive SPM that yields its approximation guarantees against an optimal adaptive SPM – this implies that the adaptivity gap in SPMs vanishes as K becomes larger. 1

Abstract. In a unit-demand multi-unit multi-item auction, an auctioneer is selling a collection of different items to a set of agents each interested in buying at most unit. Each agent has a different private value for each of the items. We consider the problem of designing a truthful auction that maximizes the auctioneer’s profit in this setting. Previously, there has been progress on this problem in the setting in which each value is drawn from a known prior distribution. Specifically, it has been shown how to design auctions tailored to these priors that achieve a constant factor approximation ratio [2, 5]. In this paper, we present a prior-independent auction for this setting. This auction is guaranteed to achieve a constant fraction of the optimal expected profit for a large class of, so called, “regular ” distributions, without specific knowledge of the distributions. 1

The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent approach for designing incentive compatible mechanisms, namely that of Vickrey, Clarke, and Groves; and the central approach for circumventing computational obstacles, that of approximation algorithms, are fundamentally incompatible: natural applications of the VCG approach to an approximation algorithm fails to yield an incentive compatible mechanism. We consider relaxing the desideratum of (ex post) incentive compatibility (IC) to Bayesian incentive compatibility (BIC), where truthtelling is a Bayes-Nash equilibrium (the standard notion of incentive compatibility in economics). For welfare maximization in single-parameter agent settings, we give a general blackbox reduction that turns any approximation algorithm into a Bayesian incentive compatible mechanism with essentially the same 1 approximation factor.

We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent’s utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This discontinuity in the utility function presents a significant challenge in the design of good mechanisms, and classical “unconstrained ” mechanisms fail to work in settings with budgets. The goal of this paper is to develop general reductions from budget-constrained Bayesian MD to unconstrained Bayesian MD with small loss in performance. We consider this question in the context of the two most well-studied objectives in mechanism design—social welfare and revenue—and present constant factor approximations in a number of settings. Some of our results extend to settings where budgets are private and agents need to be incentivized to reveal them truthfully.

With the advent of social networks such as Facebook and LinkedIn, and online offers/deals web sites, network externalties raise the possibility of marketing and advertising to users based on influence they derive from their neighbors in such networks. Indeed, a user’s knowledge of which of his neighbors “liked ” the product, changes his valuation for the product. Much of the work on the mechanism design under network externalities has addressed the setting when there is only one product. We consider a more natural setting when there are multiple competing products, and each node in the network is a unit-demand agent. We first consider the problem of welfare maximization under various different types of externality functions. Specifically we get a O(lognlog(nm)) approximation for concave externality functions, 2 O(d)-approximation for convex externality functions that are bounded above by a polynomial of degree d, and we give a O(log 3 n)-approximation when the externality function is submodular. Our techniques involve formulating non-trivial linear relaxations in each case, and developing novel rounding schemes that yield bounds vastly superior to those obtainable by directly applying results from combinatorial welfare maximization. We then consider the problem of Nash equilibrium where each node in the network is a player whose strategy space corresponds to selecting an item. We develop tight characterization of the conditions under which a Nash equilibrium exists in this game. Lastly, we consider the question of pricing and revenue optimization

We solve the optimal multi-dimensional mechanism design problem when either the number of bidders is a constant or the number of items is a constant. In the first setting, we need that the values of each bidder for the items are i.i.d., but allow different distributions for each bidder. In the second setting, we allow the values of each bidder for the items to be arbitrarily correlated, but assume that the bidders are i.i.d. For all ɛ> 0, we obtain an efficient additive ɛ-approximation, when the value distributions are bounded, or a multiplicative (1−ɛ)-approximation when the value distributions are unbounded, but satisfy the Monotone Hazard Rate condition. When there is a single bidder, we generalize these results to independent but not necessarily identically distributed value distributions, and to independent regular distributions.

Brands and agencies use marketing as a tool to influence customers. One of the major decisions in a marketing plan deals with the allocation of a given budget among media channels in order to maximize the impact on a set of potential customers. A similar situation occurs in a social network, where a marketing budget needs to be distributed among a set of potential influencers in a way that provides high-impact. We introduce several probabilistic models to capture the above scenarios. The common setting of these models consists of a bipartite graph of source and target nodes. The objective is to allocate a fixed budget among the source nodes to maximize the expected number of influenced target nodes. The concrete way in which source nodes influence target nodes depends on the underlying model. We primarily consider two models: a source-side influence model, in which a source node that is allocated a budget of k makes k independent trials to influence each of its neighboring target nodes, and a target-side influence model, in which a target node becomes influenced according to a specified rule that depends on the overall budget allocated to its neighbors. Our main results are an optimal (1 − 1/e)-approximation algorithm for the source-side model, and several inapproximability results for the target-side model, establishing that influence maximization in the latter model is provably harder.

We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multi-dimensional preferences over several possible configurations of the good (furthermore, it allows an agent’s budget and risk preference to be known only privately to the agent). These are the main challenge areas for auction theory. A single-agent problem is to optimize a given objective subject to a constraint on the maximum probability with which each type is allocated, a.k.a., an allocation rule. Our approach is a reduction from multi-agent mechanism design problem to collection of single-agent problems. We focus on maximizing revenue, but our results can be applied to other objectives (e.g., welfare). An optimal multi-agent mechanism can be computed by a linear/convex program on interim allocation rules by simultaneously optimizing several single-agent mechanisms subject to joint feasibility of the allocation rules. For single-unit auctions, Border (1991) showed that the space of all jointly feasible interim allocation rules for n agents is a D-dimensional convex polytope which can be specified by 2D linear constraints, where D is the total number of all agents’