A remark on the number of trading posts in strategic market games

In market games the one to one correspondence between commodity types and trading posts would be justified if it were true that the set of equilibria is not affected by the number of trading posts postulated at the outset of the model. We show that this is not true. We develop an example which features equilibria where a commodity is simultaneously exchanged in two trading posts at different prices, i.e., equilibria where the 'law of one price' fails when the one to one correspondence between commodities and trading posts is abandoned. Thus, we conclude that the set of equilibria in market games depends non-trivially on the number of trading posts. This conclusion further suggests that an explanation of the structure of trading posts is necessary.