Nash bargaining game

Today was a huge succes. First I won 900 forints in the Kombinatorika seminar (no, I did not need to be smart, just shameless) of which I had to use 600 to pay back my beer debt and from the remaining amount I could get a beer at mister for 210. Then I managed to lie to Telenor that my ID was also stolen and forge the signiture of the original owner of my stolen SIM-card, so now I only need a phone and you can start calling me again.

Christian Borgs gave a talk on Nash bargaining games. He presented a localization of the algorithm achieved by Kleinberg and Tardos. I think their paper is the best read to understand the problem.

My question is the following. Is it possible that if we delete the uv edge from the graph then $\gamma_v$ grows, i.e. by declaring that you do not trade with one of your possible partners, can you increase your income?