We propose an artificial intelligence problem called 'User Intention Market for Multi-Agent Navigation' which is a real problem in engineering context and also should be analyzed in economic context. The purpose of multi-agent navigation is to improve the performance of whole multi-user system without forcing them to make effort for the goal of the whole system. Although some negotiation and adjustment mechanism is needed, we analyze traditional planning techniques in artificial intelligence is not sufficient even when geometric reasoning is joined to it. We think some market mechanism has a possibility to work well. The nature of market mechanism, however, obliges users to take effort to make pricing for a service. Instead of introducing regular market mechanism, does 'user intention market' where exchange of users’ intention without currency as catalyst work well for the purpose ? This question is another problem we would like to propose in this paper.