Playing with ghosts in a Dynkin game

• We study a class of two-player optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that if the underlying process is a R-d-valued, continuous, strong Markov process, and the stopping payoff is a continuous function (with mild integrability properties) there exists a Nash equilibrium in randomised stopping times for the game. Moreover, the equilibrium strategies and the expected payoffs of the two players are computed explicitly in terms of the corresponding one-player game. To the best of our knowledge this is the first paper to address this version of Dynkin games.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Dynkin games

Uncertain competition

Randomised strategies

Nash equilibria

Reflecting strategies

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)