This paper proposes a new one-sided matching market model in which every agent has a cost function that is allowed to take a negative value. Our model aims to capture the situation where some agents can profit by exchanging their obtained goods with other agents. We formulate such a model based on a graphical one-sided matching market, introduced by Massand and Simon [Massand and Simon, IJCAI 2019]. We examine the existence of stable outcomes for such a market. We prove that there is an instance that has no core-stable allocation. On the other hand, we guarantee the existence of two-stable allocations even where exchange costs exist. However, it is PLS-hard to find a two-stable allocation for a market with exchange costs even if the maximum degree of the graph is five.

翻译：本文提出了一种新的单边匹配市场模型，其中每个智能体具有一个允许取负值的成本函数。我们的模型旨在刻画某些智能体可通过与其他智能体交换所获商品而获利的场景。我们基于Massand和Simon提出的图形化单边匹配市场[Massand and Simon, IJCAI 2019]建立了此类模型。我们研究了该市场中稳定结果的存在性。证明存在一个没有核稳定配置的实例。另一方面，我们保证了即便存在交易成本时，双稳定配置的存在性。然而，即便在图的最高度为五的情况下，为具有交易成本的市场寻找双稳定配置仍属于PLS难问题。