We formulate a notion of doubly reflected BSDE in the case where the barriers ξ

and ζ do not satisfy any regularity assumption. Under a technical assumption (a

Mokobodzki-type condition), we show existence and uniqueness of the solution. In the

case where ξ is right upper-semicontinuous and ζ is right lower-semicontinuous, the

solution is characterized in terms of the value of a corresponding $\mathcal{E}$^ƒ -Dynkin game,

i.e. a game problem over stopping times with (non-linear) ƒ-expectation, where ƒ is

the driver of the doubly reflected BSDE. In the general case where the barriers do

not satisfy any regularity assumptions, the solution of the doubly reflected BSDE is

related to the value of "an extension" of the previous non-linear game problem over a

larger set of "stopping strategies" than the set of stopping times. This characterization

is then used to establish a comparison result and a priori estimates with universal

constants.