A self-contained karma economy for the dynamic allocation of common resources

This paper presents karma mechanisms, a novel approach to the repeated allocation of a scarce resource among competing agents over an infinite time. Examples of such resource allocation problems include deciding which trip requests to serve in a ride-hailing platform during peak demand, granting the right of way in intersections, or admitting internet content to a fast channel for improved quality of service. We study a simplified yet insightful formulation of these problems where at every time two agents from a large population get randomly matched to compete over the resource. The intuitive interpretation of a karma mechanism is "If I give in now, I will be rewarded in the future." Agents compete in an auction-like setting where they bid units of karma, which circulates directly among them and is self-contained in the system. We demonstrate that this allows a society of self-interested agents to achieve high levels of efficiency without resorting to a (possibly problematic) monetary pricing of the resource. We model karma mechanisms as dynamic population games, in which agents have private states - their urgency to acquire the resource and how much karma they have - that vary in time based on their strategic decisions. We adopt the stationary Nash equilibrium as the solution concept and prove its existence. We then analyze the performance at the stationary Nash equilibrium numerically. For the case where the agents have homogeneous preferences, we compare different mechanism design choices which allow to strike trade-offs between efficiency and fairness metrics, showing how it is possible to achieve an efficient and ex-post fair allocation when the agents are future aware. Finally, we test the robustness of the mechanisms against heterogeneity in the urgency processes and the future awareness of the agents and propose remedies to some of the observed phenomena via karma redistribution.