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 investigate 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，其中每个主体都具有一个允许取负值的成本函数。该模型旨在刻画某些主体可通过与其他主体交换所得商品来获利的场景。我们基于Massand和Simon提出的图论单边匹配市场框架[Massand and Simon, IJCAI 2019]对该模型进行了形式化建模，并研究了此类市场中稳定结果的存在性问题。我们证明了存在一个不存在核稳定分配的实例。另一方面，我们保证了即便存在交易成本时，二稳定分配的存在性。然而，即使图的最大度为五，寻找具有交易成本市场的二稳定分配仍属PLS-难问题。