Well-posedness of deterministic bilevel games through a general stochastic approach

We propose a novel approach for bilevel games, called the stochastic approach, which solves the ambiguity that arises when optimal responses of followers are not unique. This model provides a spectrum of alternatives between the classic optimistic and pessimistic approaches. We model how leaders anticipate the followers' reaction as decision-dependent probability distributions, which we call beliefs. Several existence results are provided for this new approach, particularly for bilevel games with a single follower.