Achieving Efficient Collaboration in Decentralized Heterogeneous Teams using Common-Pool Resource Games

Abstract

We consider a team of heterogeneous agents that is collectively responsible for servicing and subsequently reviewing a stream of homogeneous tasks. Each agent (autonomous system or human operator) has an associated mean service time and mean review time for servicing and reviewing the tasks, respectively, which are based on their expertise and skill-sets. The team objective is to collaboratively maximize the number of serviced and reviewed tasks. To this end, we formulate a Common-Pool Resource (CPR) game and design utility functions to incentivize collaboration among team-members. We show the existence and uniqueness of the Pure Nash Equilibrium (PNE) for the CPR game. Additionally, we characterize the structure of the PNE and study the effect of heterogeneity among the agents at the PNE. We show that the formulated CPR game is a best response potential game for which both sequential best response dynamics and simultaneous best reply dynamics converge to the Nash equilibrium. Finally, we numerically illustrate the price of anarchy for the PNE.