Karma games: A decentralized, efficient and fair resource allocation scheme

Abstract

Karma games are a novel approach to the allocation of a finite resource among competing agents, such as the right of way in an intersection. The intuitive interpretation of a karma game mechanism is “If I give in now, I will be rewarded in the future”. Agents compete in an auction-like setting but instead of bidding monetary values, they bid 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 and fairness. The karma game is modeled as a new class of dynamic population games, in which agents transition between populations based on their strategic decisions. We formulate a general theory of these games, including a characterization of the new notion of the stationary Nash equilibrium, which is guaranteed to exist. An equivalency between dynamic population games and classical population games is established, which we utilize to adapt evolutionary dynamics for equilibrium computation. A numerical analysis of the karma game shows that it achieves high levels of efficiency and fairness. Further, we see a number of relatable behaviours emerge as equilibria, which exposes the potential of this new formulation to model many other complex societal behaviours.