Delay and Haircuts in Sovereign Debt - University of St Andrews

We begin at t = 2. First, let us consider the case in which the debtor is
Optimistic. Let x L and x O denote the payo¤s for the Optimistic debtor when
the creditor and the Optimistic debtor are the proposers, respectively and
let x L and x O denote the share of the available bargaining surplus for
the creditor when the creditor and the Optimistic debtor are the proposer,
respectively. Using the standard arguments 20 , to compute the payo¤s for
the creditor and the Optimistic debtor, the following two equations need to
be solved:
x L = 2 (x L + x O ) ;
(A1)
x O = 2 ( x L + x O ) ; (A2)
where denotes the common discount factor. Equations (A1) and (A2) have
a unique solution, given by (x O ; x L ):
x O = 2
2 and x L = 2 : (A3)
According to (A3), at t = 2, if the Optimistic debtor is a proposer, she
o¤ers x O = 2
to the creditor and if it is the creditor who is the proposer,
the creditor’s o¤er is x L = 2
. Given that each negotiating party has an
equal probability of being the proposer, it follows that the expected payo¤s
for the Optimistic debtor and the creditor at t = 2 are given by 2 ; 2
,
respectively.
Next, we consider the case in which the debtor is Cautious. The Cautious
debtor has concern about the sustainability of any debt settlement. The
presence of such sustainability constraint reduces the amount of bargaining
surplus that is available for debt restructuring negotiation from to
Let ~x L and ~x C denote the payo¤s for the Cautious debtor when the creditor
and the Cautious debtor are the proposers, respectively, and let (
~x L and ( s) ~x C be the share of the available bargaining surplus for
the creditor when the creditor and the Cautious debtor are the proposers,
respectively. Using the same logic as above, when the Cautious debtor is the
proposer, she always o¤er ( s) ~x ( s)
C
=
2
to the creditor, while, if the
20 Such arguments are as follows. In the equilibrium, either party will agree to a debt
restructuring proposal if the proposal o¤ers the party at least as much in discounted
present value term as it can expect to attain by waiting until the next period, given the
strategies of both parties.
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s)
s.