This paper proposes an expected return model for linear bilevel problems with uncertain reaction from follower. Using double penalty functions, the bilevel problem is transformed into a single level optimization problem. A global optimization procedure is developed to find the optimal decision. It is shown that using this model, the degree of co operation from the follower plays a key role for the leader to determine his optimal strategy, and that the follower with a partial co operation with the leader may have his most favorlte outcome