  We first study an optimal stopping problem in which a player (an agent) uses
a discrete stopping time in order to stop optimally a payoff process whose risk
is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum
game on discrete stopping times with two agents who aim at minimizing their
respective risks. The payoffs of the agents are assessed by g-expectations
(with possibly different drivers for the different players). By using the
results of the first part, combined with some ideas of S. Hamad{\`e}ne and J.
Zhang, we construct a Nash equilibrium point of this game by a recursive
procedure. Our results are obtained in the case of a standard Lipschitz driver
$g$ without any additional assumption on the driver besides that ensuring the
monotonicity of the corresponding $g$-expectation.
