Decreasing Serial Cost Sharing under Economies to Scale

We consider the problem of cost sharing in the presence of increasing returns to scale and potential strategic behavior on the part of consumers. We show that any smooth and strictly monotonic mechanism for which a Nash equilibrium exists for all profiles of convex and monotonic preferences must be dictatorial. However, we propose a cost sharing mechanism, the decreasing serial mechanism, for which an interesting domain restriction ensures existence of a noncooperative equilibrium for its cost sharing game. A characterization theorem of the mechanism based on the strategic properties of existence, uniqueness, and efficiency of its noncooperative equilibrium is provided.Publicad

Data games. Sharing public goods with exclusion.

A group of agents considers collaborating on a project which requires putting together elements owned by some of them. These elements are pure public goods with exclusion i.e. nonrival but excludable goods like for instance knowledge, data or information, patents or copyrights. The present paper addresses the question of how should agents be compensated for the goods they own. It is shown that this problem can be framed as a cost sharing game – called "data game" – to which standard cost sharing rules like the Shapley value or the nucleolus can then be applied and compared.cost sharing, compensation, Shapley value.

Data games. Sharing public goods with exclusion

A group of agents considers collaborating on a project which requires putting together elements owned by some of them. These elements are pure public goods with exclusion i.e. nonrival but excludable goods like for instance knowledge, data or information, patents or copyrights. The present paper addresses the question of how should agents be compensated for the goods they own. It is shown that this problem can be framed as a cost sharing game - called ‘data game’ - to which standard cost sharing rules like the Shapley value or the nucleolus can then be applied and compared.Cost sharing, compensation, Shapley value

Cooperative provision of indivisible public goods

A community faces the obligation of providing an indivisible public good. Each member is capable of providing it at a certain cost and the solution is to rely on the player who can do it at the lowest cost. It is then natural that he or she be compensated by the other players. The question is to know how much they should each contribute. We model this compensation problem as a cost sharing game to which standard allocation rules are applied and related to the solution resulting from the auction procedures proposed by Kleindorfer and Sertel (1994).public goods, cost sharing, core, nucleolus, Shapley value

OPTIMAL SHARING OF SURGICAL COSTS IN THE PRESENCE OF QUEUES

We deal with a cost allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context with several medical procedures, a certain demand of treatment and a maximum average waiting time guarantee set by the government. We show that sharing the use of an operating theatre to treat the patients of the different procedures, leads to a cost reduction. Then, we compute an optimal fee per procedure for the use of the operating theatre, based on the Shapley value. Afterwards, considering the post-operative time, we characterize the conditions under which this cooperation among treatments has a positive impact on the average post-operative costs. Finally, we provide a numerical example constructed on the basis of real data, to highlight the main features of our model.Surgical Waiting Lists; Queueing Theory; Cost-Sharing Game.

Data games: Sharing public goods with exclusion.

A group of firms decides to cooperate on a project that requires a combination of inputs held by some of them. These inputs are non-rival but excludable goods i.e. public goods with exclusion such as knowledge, data or information, patents or copyrights. We address the question of how firms should be compensated for the inputs they contribute. We show that this problem can be framed within a cost sharing game whose Shapley comes out as a natural solution. The main result concerns the regular structure of the core that enables a simple characterization of the nucleolus. However, compared to the Shapley value, the nucleolus defines compensations that appear to be less appropriate in the context of data sharing. Our analysis is inspired by the problem faced by the European chemical firms within the regulation program REACH that requires submission by 2018 of a detailed analysis of the substances they produce, import or use.cost sharing, Shapley value, core, nucleolus.

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

Designing Network Protocols for Good Equilibria

Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs