Dynkin Game with Asymmetric Information

Recursive construction of a Nash equilibrium in a two-player nonzero-sum stopping game with asymmetric information

“…Lempa et al [22] considered a stopping game with a finite-horizon which is an exponentially distributed random variable, where only one player is exposed to the value of this random variable. Esmaeeli et al [9] and Grün [11] presented two models in which the asymmetry of information is modelled as in the classical work of Aumann and Maschler [3]. Namely, there is a finite set of states of nature in which the game can take place.…”

Optimal stopping games in models with various information flows

“…Gensbittel and Grün [31] considered a simpler version of such a game in a model in which the dynamics of the underlying process are modelled by continuous-time Markov chains. The asymmetry of information in other models for such optimal stopping games was described in Lempa and Matomäki [44] by a random time horizon which is independent of the underlying process, in Ekström, Glover, and Leniec [17] by heterogeneous beliefs about the drift of the underlying diffusion process, in Esmaeeli, Imkeller, and Nzengang [22] by a random variable which is not necessarily independent of the underlying process, and in De Angelis, Ekström, and Glover [13] by a Bernoulli random variable affecting the drift of the underlying process only at the initial time (see also De Angelis, Gensbittel, and Villeneuve [14] for a similar problem where both players have partial information). In our model, the asymmetry of information is described by a continuous-time Markov chain which is independent of the standard Brownian motion driving the underlying process.…”

Dynkin games with incomplete and asymmetric information

“…Another formulation of asymmetric information within a Dynkin game was treated in [19], who provided conditions for the existence of a Nash equilibrium in stopping times for a setting where learning for the uninformed player is not considered. In [19] both players use stopping times, although those of the informed player are taken with respect to a larger filtration which includes extra information on the structure of the game. Randomisation is not needed in their setting because the informed player does not need to hide the information.…”

“…Randomisation is not needed in their setting because the informed player does not need to hide the information. It is indeed stated in Section 3.1, p. 288, of [19] that the uninformed player 'does not care about' or 'is not allowed to use' the additional information. This stands in sharp contrast with our setting (as well as that of [23,22], among others).…”

“…In comparison to [16] and [19], where the set-up involves no learning, and [23] and [22], where the players learn only from the actions of the opponent, our players are faced with a more complex, two-source, learning situation. In particular, the uninformed player learns about the drift of the underlying process by continuous observations of the process itself and from the actions of the informed player.…”