Sharing Non-Anonymous Costs of Multiple Resources Optimally

In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only local information of the resource's cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users

Approximately Socially-Optimal Decentralized Coalition Formation

Coalition formation is a central part of social interactions. In the emerging era of social peer-to-peer interactions (e.g., sharing economy), coalition formation will be often carried out in a decentralized manner, based on participants' individual preferences. A likely outcome will be a stable coalition structure, where no group of participants could cooperatively opt out to form another coalition that induces higher preferences to all its members. Remarkably, there exist a number of fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games) that model practical cost-sharing applications with desirable properties, such as the existence of a stable coalition structure with a small strong price-of-anarchy (SPoA) to approximate the social optimum. In this paper, we close several gaps on the previous results of decentralized coalition formation: (1) We establish a logarithmic lower bound on SPoA, and hence, show several previously known fair cost-sharing mechanisms are the best practical mechanisms with minimal SPoA. (2) We improve the SPoA of egalitarian and Nash bargaining cost-sharing mechanisms to match the lower bound. (3) We derive the SPoA of a mix of different cost-sharing mechanisms. (4) We present a decentralized algorithm to form a stable coalition structure. (5) Finally, we apply our results to a novel application of peer-to-peer energy sharing that allows households to jointly utilize mutual energy resources. We also present and analyze an empirical study of decentralized coalition formation in a real-world P2P energy sharing project

Decentralized Ride-Sharing and Vehicle-Pooling Based on Fair Cost-Sharing Mechanisms

Ride-sharing or vehicle-pooling allows commuters to team up spontaneously for transportation cost sharing. This has become a popular trend in the emerging paradigm of sharing economy. One crucial component to support effective ride-sharing is the matching mechanism that pairs up suitable commuters. Traditionally, matching has been performed in a centralized manner, whereby an operator arranges ride-sharing according to a global objective (e.g., total cost of all commuters). However, ride-sharing is a decentralized decision-making paradigm, where commuters are self-interested and only motivated to team up based on individual payments. Particularly, it is not clear how transportation cost should be shared fairly between commuters, and what ramifications of cost-sharing are on decentralized ride-sharing. This paper sheds light on the principles of decentralized ride-sharing and vehicle-pooling mechanisms based on stable matching, such that no one would be better off to deviate from a stable matching outcome. We study various fair cost-sharing mechanisms and the induced stable matching outcomes. We compare the stable matching outcomes with a social optimal outcome (that minimizes total cost) by theoretical bounds of social optimality ratios, and show that several fair cost-sharing mechanisms can achieve high social optimality. We also corroborate our results with an empirical study of taxi sharing under fair cost-sharing mechanisms by a data analysis on New York City taxi trip dataset, and provide useful insights on effective decentralized mechanisms for practical ride-sharing and vehicle-pooling.Comment: To appear in IEEE Trans. on Intelligent Transportation System

A Characterization of Undirected Graphs Admitting Optimal Cost Shares

In a seminal paper, Chen, Roughgarden and Valiant studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. One of the most intriguing open problems to date is to understand the power of budget-balanced and separable cost sharing protocols in order to induce low-cost Steiner forests. In this work, we focus on undirected networks and analyze topological properties of the underlying graph so that an optimal Steiner forest can be implemented as a Nash equilibrium (by some separable cost sharing protocol) independent of the edge costs. We term a graph efficient if the above stated property holds. As our main result, we give a complete characterization of efficient undirected graphs for two-player network design games: an undirected graph is efficient if and only if it does not contain (at least) one out of few forbidden subgraphs. Our characterization implies that several graph classes are efficient: generalized series-parallel graphs, fan and wheel graphs and graphs with small cycles.Comment: 60 pages, 69 figures, OR 2017 Berlin, WINE 2017 Bangalor