Two simple and attractive mechanisms for the fair division of indivisible goods in an online setting are LIKE and BALANCED LIKE. We study some fundamental computational problems concerning the outcomes of these mechanisms. In particular, we consider what expected outcomes are possible, what outcomes are necessary, and how to compute their exact outcomes. In general, we show that such questions are more tractable to compute for LIKE than for BALANCED LIKE. As LIKE is strategy-proof but BALANCED LIKE is not, we also consider the computational problem of how, with BALANCED LIKE, an agent can compute a strategic bid to improve their outcome. We prove that this problem is intractable in general.

中文翻译：

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在线公平分部的预期结果和操作

在在线环境中公平分配不可分割商品的两种简单而有吸引力的机制是 LIKE 和 BALANCED LIKE。我们研究了与这些机制的结果有关的一些基本计算问题。我们特别考虑哪些预期结果是可能的，哪些结果是必要的，以及如何计算它们的确切结果。总的来说，我们表明这些问题对于 LIKE 比 BALANCED LIKE 更容易计算。由于 LIKE 是策略证明，但 BALANCED LIKE 不是，我们还考虑了计算问题，即使用 BALANCED LIKE，代理如何计算战略出价以改善其结果。我们证明这个问题一般是难以解决的。