Finding trading cycles
I'm assuming that items are always traded 1-for-1.


  How do I find the longest possible series (or path) of supply &amp; demand matching among some people and therefore can foster an exchange?"


If you are only looking for one long path, then you are looking for a Hamiltonian circuit if one exists, so the decision version of the problem is NP-complete.  If you are open to having multiple disjoint cycles of exchange and just looking for as many items as possible involved in the exchange, then it is the MAX SIZE EXCHANGE problem from the Kidney Exchange literature, and it is solvable in polynomial time.



P. Biro, D. F. Manlove, and R. Rizzi. Maximum weight cycle packing in
directed graphs, with application to kidney exchange programs. Discrete
Mathematics, Algorithms and Applications, 1(04):499–517, 2009.