In this paper the alternating offer model with an exogenous risk of br
eakdown is taken to explicitly model the bargaining process underlying
the variable threat game (Nash, Econometrica, 1953). A modified versi
on of the variable threat game without commitment is also analysed wit
hin a dynamic context. The limit set of subgame perfect equilibria is
characterized in both dynamic versions. The analysis gives rise to dif
ferent results than in the two standard models. By making additional a
ssumptions the original results can be regained, indicating that these
are implicitly present in the standard analysis.