Distributed $n$-Player Approachability and Consensus in Coalitional Games

We study a distributed allocation process where, at each time, every player: i) proposes a new bid based on the average utilities produced up to that time, ii) adjusts such allocations based on the inputs received from its neighbors, and iii) generates and allocates new utilities. 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 makes the grand coalition stable.