In this paper, we study a two-sided labor market that couples the classical Fisher market with goods and the Fisher market with bads into a single unified framework. In our model, users demand tasks in order to derive utility, while workers supply labor to perform these tasks in exchange for earnings. Each task thus plays a dual role: it is a good for the user side of the market and a chore for the worker side. Given prices for tasks, users choose utility-maximizing bundles subject to budgets, while workers choose disutility-minimizing task bundles subject to earning requirements; the resulting choices induce demand and supply endogenously for each task, and a CE corresponds to prices at which these coincide. We show that such markets are guaranteed to admit a CE in a very general setting, and the first and second welfare theorems hold for our labor market model. We next study the computation of equilibria under linear preferences. We show that, similar to the chores setting, equilibria correspond to KKT points of an Eisenberg-Gale-like non-convex program. Despite the non-convex characterization, we go on to show a set of surprisingly positive results. First, we show that there exists a polynomial-time combinatorial algorithm for computing CE, which relies on a natural Walrasian scheme for updating prices. In the "CEEI-like" case, this yields a strongly polynomial-time algorithm. We next show that our market admits a natural dual program, and this non-convex labor-market program admits a change of variables that transforms it into a linear program (albeit with irrational coefficients). Finally, leveraging this LP, we give yet another polynomial-time algorithm while deriving an approach for addressing the irrational coefficients in an efficient manner. We note that, even for goods-only linear Fisher markets, obtaining such an LP formulation remains open.

翻译：摘要：本文研究了一种双边劳动力市场，该市场将经典的费雪商品市场与费雪厌恶品市场整合到一个统一框架中。在我们的模型中，用户需求任务以获取效用，而工人提供劳动以执行这些任务来换取收入。因此，每个任务扮演双重角色：对市场中的用户方是商品，对工人方则是家务。给定任务价格，用户在预算约束下选择效用最大化的任务组合，而工人在收入要求约束下选择负效用最小化的任务组合；这些选择内生地决定了每个任务的需求与供给，竞争均衡即对应使二者相等的价格。我们证明，在非常一般的设定下，此类市场必然存在竞争均衡，且第一、第二福利定理在我们的劳动力市场模型中成立。随后，我们研究线性偏好下均衡的计算。我们证明：与家务环境类似，均衡对应于类艾森伯格-盖尔非凸规划中的KKT点。尽管存在非凸性刻画，我们却得到一系列令人惊讶的积极结果。首先，我们提出一种多项式时间组合算法来计算竞争均衡，该算法依赖于一种自然的瓦尔拉斯式价格更新机制。在"类CEEI"情形下，这进一步得到强多项式时间算法。其次，我们证明该市场存在自然的对偶规划，且此非凸劳动力市场规划可通过变量替换转化为线性规划（尽管系数为无理数）。最后，利用该线性规划，我们给出另一种多项式时间算法，并推导出一种有效处理无理系数的方案。值得注意的是，即便对于纯商品线性费雪市场，获得此类线性规划表述仍是未解问题。