In the context of the stable roommates problem, it is shown that acyclicity of preferences is equivalent to the existence of symmetric utility functions, i.e. the utility of agent i when matched with j is the same as j's utility when matched with i

We analyzed the market for indivisible, pure status goods. Firms produce and sell different brands of pure status goods to a population that is willing to signal individual abilities to potential matches in another population. Individual status is determined by the most expensive status good one...