Convergence Time to Nash Equilibrium in Selfish Bin Packing

Abstract

We consider a game-theoretic bin packing problem and we study the convergence time to a Nash equilibrium. We show that, if the best-response strategy is used, then the number of steps needed to reach Nash equilibrium is O(mwmax2+nwmax) and O(nkwmax), where n, m, k and wmax denotes, resp., the number of items, the number of bins, the number of distinct item sizes, and the size of a largest item.