Socially efficient mechanism on the minimum budget

In social decision-making among strategic agents, a universal focus lies on the balance between social and individual interests. Socially efficient mechanisms are thus desirably designed to not only maximize the social welfare but also incentivize the agents for their own profit. Under a generalized model that includes applications such as double auctions and trading networks, this study establishes a socially efficient (SE), dominant-strategy incentive compatible (DSIC), and individually rational (IR) mechanism with the minimum total budget expensed to the agents. The present method exploits discrete and known type domains to reduce a set of constraints into the shortest path problem in a weighted graph. In addition to theoretical derivation, we substantiate the optimality of the proposed mechanism through numerical experiments, where it certifies strictly lower budget than Vickery-Clarke-Groves (VCG) mechanisms for a wide class of instances.