The policy bargaining model extends the alternating offer model and ca
ptures situations in which two players interact strategically with eac
h other over time and simultaneously negotiate for a binding joint pol
icy to replace competition. The assumption of a non-linear Pareto fron
tier causes several mathematical problems which are related to non-con
vex bargaining problems. The necessary and sufficient conditions for u
niqueness are derived and the set of subgame perfect equilibrium payof
fs are fully characterized. For the prisoner's dilemma a folk theorem
result is obtained. Another example shows that uniqueness is also poss
ible.