Constrained consensus for bargaining in dynamic coalitional TU games

Abstract

Abstract-We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.

Distributed n-player approachability via time and space average consensus

“…In this paper we consider coalitional TU games in which there is no central coordinator, so that players have to negotiate among themselves how to allocate rewards. In particular, each player can communicate only with neighboring players according to a neighbor graph and generates, at each communication round, a vector of players' rewards (see also the distributed allocation processes in Nedić and Bauso (2011)). The objective is that all the agents reach asymptotically a common (temporal) average reward that lies in the core of the game.…”