With the growing use of distributed machine learning techniques, there is a growing need for data markets that allows agents to share data with each other. Nevertheless data has unique features that separates it from other commodities including replicability, cost of sharing, and ability to distort. We study a setup where each agent can be both buyer and seller of data. For this setup, we consider two cases: bilateral data exchange (trading data with data) and unilateral data exchange (trading data with money). We model bilateral sharing as a network formation game and show the existence of strongly stable outcome under the top agents property by allowing limited complementarity. We propose ordered match algorithm which can find the stable outcome in O(N^2) (N is the number of agents). For the unilateral sharing, under the assumption of additive cost structure, we construct competitive prices that can implement any social welfare maximizing outcome. Finally for this setup when agents have private information, we propose mixed-VCG mechanism which uses zero cost data distortion of data sharing with its isolated impact to achieve budget balance while truthfully implementing socially optimal outcomes to the exact level of budget imbalance of standard VCG mechanisms. Mixed-VCG uses data distortions as data money for this purpose. We further relax zero cost data distortion assumption by proposing distorted-mixed-VCG. We also extend our model and results to data sharing via incremental inquiries and differential privacy costs.

In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have (possibly overlapping) types and (2) hospital-doctor matching where various regional quotas are imposed. In this paper, we present a polynomial-time reduction to transform an instance of (1) to an instance of (2) and we show how the feasibility and stability of corresponding matchings are preserved under the reduction. Our reduction provides a formal connection between two important strands of work on matching with distributional constraints. We then apply the reduction in two ways. Firstly, we show that it is NP-complete to check whether a feasible and stable outcome for (1) exists. Due to our reduction, these NP-completeness results carry over to setting (2). In view of this, we help unify some of the results that have been presented in the literature. Secondly, if we have positive results for (2), then we have corresponding results for (1). One key conclusion of our results is that further developments on axiomatic and algorithmic aspects of hospital-doctor matching with regional quotas will result in corresponding results for school choice with diversity constraints.

We consider a market setting in which buyers are individuals of a population, whose relationships are represented by an underlying social graph. Given buyers valuations for the items being sold, an outcome consists of a pricing of the objects and an allocation of bundles to the buyers. An outcome is social envy-free if no buyer strictly prefers the bundles of her neighbors in the social graph. We focus on the revenue maximization problem in multi-unit markets, in which there are multiple copies of a same item being sold and each buyer is assigned a set of identical items. We consider the four different cases arising by considering different buyers valuations, i.e., single-minded or general, and by adopting different forms of pricing, that is item- or bundle-pricing. For all the above cases we show the hardness of the revenue maximization problem and give corresponding approximation results. All our approximation bounds are optimal or nearly optimal. Moreover, we provide an optimal allocation algorithm for general valuations with item-pricing, under the assumption of social graphs of bounded treewidth. Finally, we determine optimal bounds on the corresponding price of envy-freeness, that is on the worst case ratio between the maximum revenue that can be achieved without envy-freeness constraints, and the one obtainable in case of social relationships. Some of our results close hardness open questions or improve already known ones in the literature concerning the classical setting without sociality.

We propose a new variant of the group activity selection problem (GASP), where the agents are placed on a social network and activities can only be assigned to connected subgroups. We show that if multiple groupscan simultaneously engage in the same activity, finding a stable outcome is easy as long as the networkis acyclic. In contrast, if each activity can be assigned to a single group only, finding stable outcomes becomes computationally intractable, even if the underlying network is very simple: the problem of determining whether a given instance of a GASP admits a Nash stable outcome turns out to be NP-hard when the social network is a path, a star, or if the size of each connected component is bounded by a constant.On the other hand, we obtain fixed-parameter tractability results for this problem with respectto the number of activities.

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given m random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.

We propose influence games, a new class of graphical games, as a model of the behavior of large but finite networked populations. Grounded in non-cooperative game theory, we introduce a new approach to the study of influence in networks that captures the strategic aspects of complex interactions in the network. We study computational problems on influence games, including the identification of the most influential nodes. We characterize the computational complexity of various problems in influence games, propose several heuristics for the hard cases, and design approximation algorithms, with provable guarantees, for the most influential nodes problem.