Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is an equilibrium-based solution concept for fair division of discrete items to agents with combinatorial demands. In theory, it is known that in asymptotically large markets: 1. For incentives, the A-CEEI mechanism is Envy-Free-but-for-Tie-Breaking (EF-TB), which implies that it is Strategyproof-in-the-Large (SP-L). 2. From a computational perspective, computing the equilibrium solution is unfortunately a computationally intractable problem (in the worst-case, assuming $\textsf{PPAD}\ne \textsf{FP}$). We develop a new heuristic algorithm that outperforms the previous state-of-the-art by multiple orders of magnitude. This new, faster algorithm lets us perform experiments on real-world inputs for the first time. We discover that with real-world preferences, even in a realistic implementation that satisfies the EF-TB and SP-L properties, agents may have surprisingly simple and plausible deviations from truthful reporting of preferences. To this end, we propose a novel strengthening of EF-TB, which dramatically reduces the potential for strategic deviations from truthful reporting in our experiments. A (variant of) our algorithm is now in production: on real course allocation problems it is much faster, has zero clearing error, and has stronger incentive properties than the prior state-of-the-art implementation.

翻译：近似等收入竞争均衡（A-CEEI）是一种基于均衡概念的解决方案，用于将离散物品公平分配给具有组合需求的智能体。理论上，在渐近大规模市场中已知：1. 从激励角度看，A-CEEI机制满足“除平局处理外无嫉妒”（EF-TB），这意味着它在大规模策略性（SP-L）中具有防操纵性。2. 从计算角度看，求解该均衡解在计算上是一个棘手问题（在最坏情况下，假设$\textsf{PPAD}\ne \textsf{FP}$）。我们提出了一种新的启发式算法，其性能比先前最优方法高出多个数量级。这一更快的新算法使我们首次能够在现实输入数据上进行实验。我们发现，在具有现实偏好的情况下，即使实现满足EF-TB和SP-L特性的实用机制，智能体仍可能采取简单且合理的策略偏离真实偏好报告。为此，我们提出了EF-TB的一种新型加强版本，在我们的实验中显著降低了策略性偏离真实报告的可能性。我们算法的（一种变体）现已投入实际应用：在处理真实课程分配问题时，它比先前最优实现具有更快的运行速度、零清算误差以及更强的激励特性。