  We prove that zero-sum Dynkin games in continuous time with partial and
asymmetric information admit a value in randomised stopping times when the
stopping payoffs of the players are general \cadlag measurable processes. As a
by-product of our method of proof we also obtain existence of optimal
strategies for both players. The main novelties are that we do not assume a
Markovian nature of the game nor a particular structure of the information
available to the players. This allows us to go beyond the variational methods
(based on PDEs) developed in the literature on Dynkin games in continuous time
with partial/asymmetric information. Instead, we focus on a probabilistic and
functional analytic approach based on the general theory of stochastic
processes and Sion's min-max theorem (M. Sion, Pacific J. Math., 8, 1958, pp.
171-176). Our framework encompasses examples found in the literature on
continuous time Dynkin games with asymmetric information and we provide
counterexamples to show that our assumptions cannot be further relaxed.
