  This paper studies a nonzero-sum Dynkin game in discrete time under
non-exponential discounting. For both players, there are two levels of
game-theoretic reasoning intertwined. First, each player looks for an
intra-personal equilibrium among her current and future selves, so as to
resolve time inconsistency triggered by non-exponential discounting. Next,
given the other player's chosen stopping policy, each player selects a best
response among her intra-personal equilibria. A resulting inter-personal
equilibrium is then a Nash equilibrium between the two players, each of whom
employs her best intra-personal equilibrium with respect to the other player's
stopping policy. Under appropriate conditions, we show that an inter-personal
equilibrium exists, based on concrete iterative procedures along with Zorn's
lemma. To illustrate our theoretic results, we investigate a two-player real
options valuation problem: two firms negotiate a deal of cooperation to
initiate a project jointly. By deriving inter-personal equilibria explicitly,
we find that coercive power in negotiation depends crucially on the impatience
levels of the two firms.
