Distributed <inline-formula> <tex-math notation="TeX">$n$</tex-math></inline-formula>-Player Approachability and Consensus in Coalitional Games

Abstract

We study a distributed allocation process where, repeatedly in time, every player renegotiates past allocations with neighbors and allocates new revenues. The average allocations evolve according to a doubly (over time and space) averaging algorithm. We study conditions under which the average allocations reach consensus to any point within a predefined target set even in the presence of adversarial disturbances. Motivations arise in the context of coalitional games with transferable utilities (TU) where the target set is any set of allocations that make the grand coalitions stable.

Bilateral Peer-to-Peer Energy Trading via Coalitional Games

“…Let us now mention the features of our algorithm that enhance its practicality.First, for the negotiation, the market participants do not require full information of the game but only the values of their own contracts represented by the bounding sets in (1), which is privacy preserving. Such a lower information requirement of our mechanism is a considerable benefit over the algorithm presented in [26], which requires each participant to have complete information of the corresponding core set in (3). Second, utilizing the half-spaces H i ∈ H i as the fixed-point sets of the operators T i ∈ T in (12) allows us to design T as a set of linear operators.…”

“…3) We develop a novel distributed negotiation mechanism presented as a fixed-point iteration where buyers-sellers communicate locally over a possibly time-varying communication network. We exploit the geometrical structure of the core solution together with operator theory to formulate our algorithm via linear operations, thus, considerably reducing the computational complexity of the negotiation, strongly improving over [25], [26]. We show that the mechanism converges to a payoff allocation in the core of the assignment game (see Section IV).…”