Local Computation Mechanism Design

We introduce the notion of local computation mechanism design —designing game-theoretic mechanisms that run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. When the mechanism employs payments, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanism needs to maintain incentive compatibility with respect to the allocation and payments. We present local computation mechanisms for two classical game-theoretical problems: stable matching and job scheduling. For stable matching, some of our techniques may have implications to the global (non-LCA (Local Computation Algorithm)) setting. Specifically, we show that when the men’s preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.