Automated Mechanism Design: Compact and Decomposition Linear Programming Models

In the context of multi-agent systems, Automated Mechanism Design (AMD) is the computer-based design of the rules of a mechanism, which reaches an equilibrium despite the fact that agents can be selfish and lie about their preferences. Although it has been shown that AMD can be modelled as a linear program, it is with an exponential number of variables and consequently, there is no known efficient algorithm. We revisit the latter linear program model proposed for the AMD problem and introduce a new one with a polynomial number of variables. We show that the latter model corresponds to a Dantzig-Wolfe decomposition of the second one and design efficient solution schemes in polynomial time for both two models. Numerical experiments compare the solution efficiency of both models and show that we can solve very significantly larger data instances than before, up to 2,000 agents or 2,000 resources in about 35 seconds.