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.

翻译：本文提出因果机制（karma mechanisms），这是一种在无限时间跨度内重复分配稀缺资源给竞争智能体的新颖方法。此类资源分配问题的实例包括：在高峰时段决定网约车平台中应满足哪些行程请求、在交叉路口赋予通行权，或允许互联网内容接入高速通道以提升服务质量。我们研究了一个简化但具有洞察力的建模框架：在每个时间步，从大规模群体中随机选取两个智能体，就资源展开竞争。因果机制的直观解释是：“若我现在让步，未来将获得回报”。智能体在类似拍卖的设定中竞标因果单位，这些单位直接在他们之间流通，并在系统中构成自足体系。我们证明，这能使由自私智能体构成的社会在不依赖（可能引发问题的）资源货币定价的前提下实现高效率。我们将因果机制建模为动态群体博弈，其中智能体拥有私有状态——他们获取资源的紧迫性及所持因果量——这些状态会随战略决策而动态变化。采用稳态纳什均衡作为解概念，并证明其存在性。随后通过数值方法分析稳态纳什均衡下的性能表现。针对智能体同质偏好情形，我们对比了不同机制设计选择在效率与公平性指标间的权衡关系，揭示了当智能体具有前瞻性时实现高效且事后公平分配的路径。最后，我们检验了机制对智能体紧迫性过程异质性与前瞻意识差异的鲁棒性，并通过因果再分配手段提出对观测现象的修正方案。