  A multi-player competitive Dynkin stopping game is constructed. Each player
can either exit the game for a fixed payoff, determined a priori, or stay and
receive an adjusted payoff depending on the decision of other players. The
single period case is shown to be "weakly unilaterally competitive". We present
an explicit construction of the unique value at which Nash and optimal
equilibria are attained. Multiple period generalisations are explored. The game
has interpretations in economic and financial contexts, for example, as a
consumption model with bounded resources. It also serves as a starting point to
the construction of multi-person financial game options. In particular, the
concept of optimal equilibria becomes pivotal in the pricing of the game
options via super-replication.
