Deterministic
Multi-Player Dynkin Games

Eilon
Solan and Nicolas Vieille

A *multi-player Dynkin game* is a
sequential game in which at every stage one of the players
is chosen, and that player
can decide whether to continue the game or to stop it,
in which case all players receive some terminal
payoff.

We study a variant of this model, where
the order by which players are chosen is deterministic,
and the probability that the game
terminates once the chosen player decides to stop may be strictly less than 1.

We prove that a subgame-perfect e-equilibrium in Markovian strategies exists.

If the game is not degenerate, this e-equilibrium is actually in pure strategies,
but in degenerate cases there need not
exist a subgame-perfect e-equilibrium in pure strategies