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：摘要: 近似等收入竞争均衡（A-CEEI）是一种基于均衡的概念，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，在渐近大市场中已知：1. 在激励方面，A-CEEI机制是“除破平外无妒忌”（EF-TB）的，这暗示其具有“大规模策略自明性”（SP-L）。2. 从计算角度看，计算均衡解在不幸情况下是计算上棘手的（在最坏情形下，假设$\textsf{PPAD}\ne \textsf{FP}$）。我们开发了一种新的启发式算法，其性能比先前最先进算法高出多个数量级。这一新加速算法使我们首次能在真实世界输入上开展实验。我们发现在真实偏好下，即使在满足EF-TB和SP-L属性的现实实现中，智能体也可能对真实汇报偏好存在令人惊讶的简单且合理的偏离。为此，我们提出了一种EF-TB的新强化版本，在我们的实验中显著减少了策略性偏离真实汇报的潜力。我们算法的一个变体现已投入生产：在真实课程分配问题上，它比先前最先进实现快得多、清算误差为零，且具有更强的激励属性。