Distributed Task Allocation for Self-Interested Agents With Partially Unknown Rewards

This article provides a novel solution to a task allocation problem, by which a group of agents assigns a discrete set of tasks in a distributed manner. In this setting, heterogeneous agents have individual preferences and associated rewards for doing each task; however, these rewards are only known asymptotically. The assignment problem is formulated by means of a combinatorial partition game for known rewards, with no constraints on the number of tasks per agent. We relax this into a weight game, which together with the former, are shown to contain the optimal task allocation in the corresponding set of Nash equilibria (NE). We then propose a projected, best-response, ascending gradient dynamics (PBRAG) that converges to an NE in finite time. This forms the basis of a distributed online version that can deal with a converging sequence of rewards by means of an agreement subroutine. We present simulations that support our results.