Distributed matching with mixed maximum-minimum utilities

In this article, we study distributed agent matching with search friction in environments characterized by costly exploration, where each agent's utility from forming a partnership is influenced by some linear combination of themaximum and the minimum among the two agents' competence. The article provides a cohesive analysis for such case, proving the equilibrium structure for the different min-max linear combinations that may be used. The article presents an extensive equilibrium analysis of such settings, proving three distinct resulting patterns of the acceptance thresholds used by the different agents. The first relates to settings where a greater emphasis is placed on the minimum type, or in the extreme case where the minimum type solely determines the output. In these cases, the assortative matching characteristic holds, where all agents set their threshold below their own type and the greater is the agent type, the greater is its threshold. When the utility from the partnership formation is solely determined by the maximum type, we show that there exists a type x where partnerships form if and only if one of the agents has a type equal to or greater than x. When a greater emphasis is placed on the maximum type (but not only), we prove that assortative matching never holds, and the change in the agents' acceptance thresholds can frequently shift from an increase to a decrease.