A novel algorithm for divisible resource allocations under PSP auction mechanism

In this paper we study the auction games for the allocation of divisible resources under the progressive second price mechanism under which the incentive compatibility holds, i.e., the truth-telling bid strategy is the best response of individual players under this mechanism. We design a novel dynamic process for the underlying PSP auction games following which the system will converge to the Nash equilibrium. More specifically, instead of directly updating individuals best response successively, proposed by Lazar and Semret, under which the convergence may not hold, we define an update policy to determine which player is allowed to update his best response in next update step, and assign an upper limit of the resource quantity which can be submitted by this player; then following the proposed update mechanism and under certain mild conditions, the auction system can converge to a Nash equilibrium which is demonstrated with numerical examples.