Recently, the idea of using local currency has been attracting attention as a way of circulating goods and services in local communities. However, if users of this currency in the same community have a variety of values, it may be difficult to circulate goods and services. For this reason, we have devised value exchange systems using a local currency embodying the variety of values for exchanging services and values. The systems studied so far increase trading in the community. However, they assume that there are only two users in a community. Moreover, users may not always be satisfied in the previous systems. In this paper, we extend our system to n users by using game theory. Moreover, we examine the condition under which all users in a community can be satisfied by using the core of game theory.