  In [1] Zawadoski introduces a banking network model in which the asset and
counter-party risks are treated separately and the banks hedge their assets
risks by appropriate OTC contracts. In his model, each bank has only two
counter-party neighbors, a bank fails due to the counter-party risk only if at
least one of its two neighbors default, and such a counter-party risk is a low
probability event. Informally, the author shows that the banks will hedge their
asset risks by appropriate OTC contracts, and, though it may be socially
optimal to insure against counter-party risk, in equilibrium banks will {\em
not} choose to insure this low probability event.
  In this paper, we consider the above model for more general network
topologies, namely when each node has exactly 2r counter-party neighbors for
some integer r>0. We extend the analysis of [1] to show that as the number of
counter-party neighbors increase the probability of counter-party risk also
increases, and in particular the socially optimal solution becomes privately
sustainable when each bank hedges its risk to at least n/2 banks, where n is
the number of banks in the network, i.e., when 2r is at least n/2, banks not
only hedge their asset risk but also hedge its counter-party risk.
