Incentivizing Collaboration in Heterogeneous Teams via Common-Pool Resource Games

We consider a team of heterogeneous agents that is collectively responsible for servicing, and subsequently reviewing, a stream of homogeneous tasks. Each agent has an associated mean service time and a mean review time for servicing and reviewing the tasks, respectively. Agents receive a reward based on their service and review admission rates. The team objective is to collaboratively maximize the number of "serviced and reviewed" tasks. We formulate a Common-Pool Resource (CPR) game and design utility functions to incentivize collaboration among heterogeneous agents in a decentralized manner. We show the existence of a unique Pure Nash Equilibrium (PNE), and establish convergence of best response dynamics to this unique PNE. Finally, we establish an analytic upper bound on three measures of inefficiency of the PNE, namely the price of anarchy, the ratio of the total review admission rate, and the ratio of latency, along with an empirical study.