  This paper presents karma mechanisms, a novel approach to the repeated
allocation of a scarce resource among competing agents over an infinite time.
Examples include deciding which ride hailing trip requests to serve during peak
demand, granting the right of way in intersections or lane mergers, or
admitting internet content to a regulated fast channel. We study a simplified
yet insightful formulation of these problems where at every instant 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 and guarantee the existence of a stationary Nash
equilibrium. We then analyze the performance at the stationary Nash equilibrium
numerically. For the case of homogeneous agents, we compare different mechanism
design choices, showing that it is possible to achieve an efficient and ex-post
fair allocation when the agents are future aware. Finally, we test the
robustness against agent heterogeneity and propose remedies to some of the
observed phenomena via karma redistribution.
