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AbstractThis 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.

The key to obtaining a mechanistic and reliable understanding of complex public opinion formation processes is to identify the main mechanism governing interpersonal influence. Researchers have long been exploring simple yet predictive mathematical models of opinion dynamics. Although most models are based on the assumption that individuals update their opinions by averaging others' opinions, researchers might need to rethink this universally adopted micro-foundation. The deceivingly simple weighted-averaging mechanism features a non-negligible unrealistic implication, which brings unnecessary difficulties in seeking a proper balance between model complexity and predictive power. In this paper, we fundamentally resolve this problem by proposing the weighted-median mechanism as a new micro-foundation of opinion dynamics. Such an inconspicuous change from averaging to median leads to rich consequences. The weighted-median mechanism, derived from the cognitive dissonance theory in psychology, is well supported by online experiment data. It also broadens the applicability of opinion dynamics models to multiple-choice issues with ordered discrete options, e.g., political elections. Moreover, comparative studies show that the weighted-median mechanism predicts various real-world patterns of opinion evolution while some widely studied averaging-based models fail to, including how group structure affects the likelihood of reaching consensus and how extreme opinions are located in social networks. ; ISSN:2643-1564