Before us is Mishnah 4 in chapter 5 of Maseches Nedarim, which contains two topics: three ways in which a person uses the language of cherem to forbid benefit between himself and his fellow, and the status of the two of them with regard to property held in common by the public.
Defining the cherem of our Mishnah:
One who says to his fellow "I am forbidden to you as cherem" does not mean the cherem given to kohanim, for that type of cherem is given to a kohen and benefit from it is permitted, so such a statement would not create a valid vow. The intent is to the cherem of bedek habayis, property consecrated to the Beis HaMikdash, and a cherem of this sort is like one who compares the item to a korban, and from this the prohibition takes effect.
The three forms of the vow:
"Hareini alecha cherem" - the one who vows forbids himself to his fellow and establishes that his fellow may not derive benefit from him. Therefore the mudar, the one who is the subject of the vow, is the one forbidden to derive benefit.
"Harei at alai cherem" - one who tells his fellow that his fellow is forbidden to him, in which case the one who vows himself is the one forbidden to derive benefit.
"Hareini alecha v'at alai" - both statements together, and both prohibitions take effect. One person made both vows, but in doing so he created a prohibition upon himself and upon his fellow alike.
Benefit from communal property:
Even though both are forbidden to one another, the Mishnah distinguishes between two categories of property:
"U'mutarin b'davar shel olei Bavel" - both are permitted to derive benefit from things in the public domain that belong to those who came up from Bavel, that is, to the public at large. These are not assets held in partnership, but rather they belong to all of Israel, and their status is like ownerless property, so they are not considered to be held by any particular person.
"V'asurin b'davar shel osah ha'ir" - if both of them live in the same city, they are forbidden to derive benefit from the things that belong to that city, since with regard to the city's assets all the residents of the city are considered partners. Once the two of them became forbidden to one another, they cannot derive benefit from property in which the other has a share.
In summary: In this Mishnah we learned that the cherem spoken of here is the cherem of bedek habayis, whose status is like that of a korban, and not the cherem of kohanim, from which benefit is permitted. "Hareini alecha" - the mudar is forbidden; "Harei at alai" - the one who vows is forbidden; "Hareini alecha v'at alai" - both are forbidden. Nevertheless, both are permitted to benefit from the assets of those who came up from Bavel, whose status is like ownerless property, and both are forbidden to benefit from the assets of that city, in which all the residents of the city are partners.