We study no-money mechanisms for allocating indivisible items to strategic agents with additive preferences under a stochastic model. In this model, items' values are drawn from an underlying distribution and mechanisms are evaluated with respect to this draw (e.g., in expectation, or with high probability). Motivated by worst-case impossibilities which show that truthfulness severely restricts fairness and efficiency, we ask whether truthful mechanisms continue to perform poorly on random instances. We first focus on dominant-strategy incentive compatible (DSIC) mechanisms. For two agents, we obtain a tight picture. Specifically, we show that there exists a distribution under which no DSIC mechanism achieves an expected welfare approximation better than $\frac{2+\sqrt{2}}{4}\approx 0.854$, and we give a DSIC mechanism that matches this bound for all distributions simultaneously. We further show that, for every distribution, there exists a DSIC mechanism that is envy-free with high probability and obtains the same welfare. A key ingredient is a new, tight connection between welfare guarantees of a family of DSIC, no-money mechanisms and i.i.d.\ prophet inequalities. This connection allows us to generalize to $n$ agents; in particular, we obtain a DSIC mechanism that achieves a $\approx 0.745$ approximation to welfare, and another DSIC mechanism achieving a $1/2$-approximation welfare that is envy-free with high probability. We then turn to Bayesian incentive compatibility (BIC). Under i.i.d.\ valuations, we show that BIC comes at essentially no cost: we design a prior-independent BIC mechanism that achieves a $(1-\varepsilon)$-approximation to the optimal welfare, while being envy-free with high probability. Under independent but non-identical priors, we obtain BIC mechanisms that are $(1-\varepsilon)$-approximately Pareto efficient and envy-free with high probability.

翻译：我们研究了在随机模型下，为具有可加性偏好的策略型智能体分配不可分割物品的无货币机制。在该模型中，物品的价值从某个基础分布中抽取，而机制的性能评估基于此抽取（例如，期望性能或以高概率性能）。受最坏情况不可能性结果的启发——这些结果表明真实性会严重限制公平性和效率——我们探讨了真实机制在随机实例上是否仍然表现不佳。我们首先关注占优策略激励相容（DSIC）机制。对于两个智能体，我们得到了一个完整的图景。具体而言，我们证明了存在一个分布，使得没有任何DSIC机制能达到优于$\frac{2+\sqrt{2}}{4}\approx 0.854$的期望福利近似比，同时我们给出了一个DSIC机制，该机制能同时对所有分布达到此界限。我们进一步证明，对于每个分布，都存在一个DSIC机制，该机制以高概率无嫉妒并取得相同的福利。一个关键要素是建立了一类DSIC无货币机制的福利保证与独立同分布先知不等式之间新的紧密联系。这一联系使我们能够将结果推广到$n$个智能体；特别地，我们得到了一个DSIC机制，其福利近似比达到约$0.745$，以及另一个DSIC机制，其福利近似比为$1/2$并以高概率无嫉妒。随后，我们转向贝叶斯激励相容（BIC）机制。在独立同分布估值下，我们证明BIC几乎不带来任何代价：我们设计了一个与先验无关的BIC机制，该机制能以高概率无嫉妒地达到最优福利的$(1-\varepsilon)$近似比。在独立但非同分布的先验下，我们得到了BIC机制，这些机制以高概率是$(1-\varepsilon)$近似帕累托有效且无嫉妒的。