  We study financial systems from a game-theoretic standpoint. A financial
system is represented by a network, where nodes correspond to firms, and
directed labeled edges correspond to debt contracts between them. The existence
of cycles in the network indicates that a payment of a firm to one of its
lenders might result to some incoming payment. So, if a firm cannot fully repay
its debt, then the exact (partial) payments it makes to each of its creditors
can affect the cash inflow back to itself. We naturally assume that the firms
are interested in their financial well-being (utility) which is aligned with
the amount of incoming payments they receive from the network. This defines a
game among the firms, that can be seen as utility-maximizing agents who can
strategize over their payments.
  We are the first to study financial network games that arise under a natural
set of payment strategies called priority-proportional payments. We investigate
the existence and (in)efficiency of equilibrium strategies, under different
assumptions on how the firms' utility is defined, on the types of debt
contracts allowed between the firms, and on the presence of other financial
features that commonly arise in practice. Surprisingly, even if all firms'
strategies are fixed, the existence of a unique payment profile is not
guaranteed. So, we also investigate the existence and computation of valid
payment profiles for fixed payment strategies.
