Distributed Auction Algorithms for the Assignment Problem with Partial Information

Abstract

Task-asset assignment is a fundamental problem paradigm in a wide variety of applications. Typical problem setting involves a single decision maker (DM) who has complete knowledge of the weight (reward, benefit, accuracy) matrix and who can control any of the assets to execute the tasks. Motivated by planning problems arising in distributed organizations, this paper introduces a novel variation of the assignment problem, wherein there are multiple DMs and each DM knows only a part of the weight matrix and/or controls a subset of the assets. We extend the auction algorithm to such realistic settings with various partial information structures using a blackboard coordination structure. We show that by communicating the bid, the best and the second best profits among DMs and with a coordinator, the DMs can reconstruct the centralized assignment solution. The auction setup provides a nice analytical framework for formalizing how team members build internal models of other DMs and achieve team cohesiveness over time.