Distributed mechanism design with learning guarantees

Mechanism design for fully strategic agents commonly assumes that messages are broadcasted between agents of the system. Moreover, for mechanism design, the stability of Nash equilibrium (NE) is demonstrated by showing convergence of specific pre-designed learning dynamics, rather than for a class of learning dynamics. In this paper, we consider the common private goods resource allocation problem: sharing K infinitely divisible resources among strategic agents for their private consumption. We present a distributed mechanism for a set of agents who communicate through a given network. In a distributed mechanism, agents' messages are not broadcast to all other agents as in the standard mechanism design framework, but are exchanged only in the local neighborhood of each agent. The presented mechanism produces a unique NE and fully implements the social welfare maximizing allocation. In addition, the mechanism is budget-balanced at NE. It is also shown that the mechanism induces a game with contractive best-response, leading to guaranteed convergence for all learning dynamics within the Adaptive Best-Response dynamics class, including dynamics such as Cournot best-response, k-period best-response and Fictitious Play. We also present a numerical study of convergence under repeated play, for various communication graphs and learning dynamics.