Efficient Distributed Resource Allocation under Synchronous Auction-based Algorithm

This work focuses on an auction-based scheme that develops a synchronous algorithm for solving resource allocation optimization problems from the perspective of efficiency, i.e. determining an allocation strategy that maximizes the social welfare. These problems are usually computationally and communicatively complex. In view of the competitive fairness with incomplete private information of players under auction games, as well as the incentive compatibility and the existence of efficient Nash Equilibrium (NE) under Vickrey-Clarke-Groves (VCG) mechanisms, we transform the considered resource allocation problems into VCG-style auction-based problems, which enable the derivation of an efficient-simultaneous iteration algorithm. Unlike those asynchronous algorithms, simultaneous updating in population size may bring greater challenges in system stability and convergence. In the proposed algorithm in this paper, each player synchronously updates his best response in an alternative feasible set at each iteration under a demand constraint associated with the submitted bid profile in last iteration. This can guarantee the advantage of monotonous increasing of the social welfare, further the convergence of the synchronous algorithm. Moreover, the system is shown to converge to the efficient NE, which is demonstrated by the numerical results.