In this paper we consider repeated coalitional games with transferable utilities (TU) over networks. Namely, we consider a set of n players that have to distribute among themselves a vector of rewards (one for each player). In our network version there is no coordinator allocating the rewards, but the agents have to agree on a common time-averaged vector by updating the local estimates of the reward vector. The common time-averaged reward vector has to approach a suitable constraint set, called core of the game, that guarantees that no agents benefit from quitting the grand coalition. We propose a doubly (over time and space) averaging distributed algorithm. At every iteration, each agent first computes a weighted average of its own time-averaged estimate and those of his neighbors and then generates a new reward vector in order to drive the time-averaged estimate towards a pre-assigned set. The main contribution of the paper is to prove that under certain assumptions, i) all agents' estimates reach consensus on the true time-averaged reward vector, and ii) the estimates (and thus the true time-averaged reward vector) approach the pre-assigned set. Conditions for this to happen are related to the connectivity over time of the communication topology and to the approachability principle.

Bauso, D., Notarstefano, G. (2012). Distributed n-player approachability via time and space average consensus. In IFAC Proceedings Volumes.

Distributed n-player approachability via time and space average consensus

BAUSO, Dario;
2012-01-01

Abstract

In this paper we consider repeated coalitional games with transferable utilities (TU) over networks. Namely, we consider a set of n players that have to distribute among themselves a vector of rewards (one for each player). In our network version there is no coordinator allocating the rewards, but the agents have to agree on a common time-averaged vector by updating the local estimates of the reward vector. The common time-averaged reward vector has to approach a suitable constraint set, called core of the game, that guarantees that no agents benefit from quitting the grand coalition. We propose a doubly (over time and space) averaging distributed algorithm. At every iteration, each agent first computes a weighted average of its own time-averaged estimate and those of his neighbors and then generates a new reward vector in order to drive the time-averaged estimate towards a pre-assigned set. The main contribution of the paper is to prove that under certain assumptions, i) all agents' estimates reach consensus on the true time-averaged reward vector, and ii) the estimates (and thus the true time-averaged reward vector) approach the pre-assigned set. Conditions for this to happen are related to the connectivity over time of the communication topology and to the approachability principle.
3rd IFAC workshop on distributed estimantion and control in networked systems
Santa Barbara, CA; United States
14 settembre 2011
4
Bauso, D., Notarstefano, G. (2012). Distributed n-player approachability via time and space average consensus. In IFAC Proceedings Volumes.
Proceedings (atti dei congressi)
Bauso, D; Notarstefano, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/77887
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