Maximal Decompositions of Cost Games into Specific and Joint Costs

The problem in which some agents joint together to realize a set of projects and must decide how to share its cost may be seen as a cooperative cost game. In many instances, total cost may naturally be decomposed into joint costs and costs that are specific to individual agents. We show that the maximal amount that can be attributed directly to each agent while yielding a problem for the joint cost that remains a cost game, is given by the minimal incremental cost of adding this agent to any of the possible coalitions of other agents. Thus, for concave games, it is given by the incremental cost of adding the agent to all others. We also show that a concave game yields a reduced game that is itself concave. Le problème où plusieurs agents entreprennent en commun un ensemble de projets et doivent décider du partage du coût total peut être vu comme un jeu coopératif. Dans certains cas, le coût total peut naturellement être décomposé en coûts joints et coûts spécifiques aux agents. On montre que le montant maximal qui peut être attribué directement à chaque agent, tout en donnant un problème de partage de coût joint qui constitue encore un jeu de coût, est donné par le minimum des coûts incrémentaux de l'adjonction de l'agent aux coalitions possibles des autres agents.Cost game, decomposition, jeu de coût, décomposition

Optimal Pilot Symbols Ratio in terms of Spectrum and Energy Efficiency in Uplink CoMP Networks

In wireless networks, Spectrum Efficiency (SE) and Energy Efficiency (EE) can be affected by the channel estimation that needs to be well designed in practice. In this paper, considering channel estimation error and non-ideal backhaul links, we optimize the pilot symbols ratio in terms of SE and EE in uplink Coordinated Multi-point (CoMP) networks. Modeling the channel estimation error, we formulate the SE and EE maximization problems by analyzing the system capacity with imperfect channel estimation. The maximal system capacity in SE optimization and the minimal transmit power in EE optimization, which both have the closed-form expressions, are derived by some reasonable approximations to reduce the complexity of solving complicated equations. Simulations are carried out to validate the superiority of our scheme, verify the accuracy of our approximation, and show the effect of pilot symbols ratio.Comment: 5 pages, 3 figures, 2017 IEEE 85th Vehicular Technology Conference (VTC Spring