Abstract We use the notion of Halpern-type sequence recently introduced by present authors to conclude two strong convergence theorems for solving bilevel equilibrium problems proposed Yuying et al. and some authors. Our result excludes assumptions as were cases in their results.

An Equilibrium Problem with an Equilibrium Constraint (EPEC) is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium in a situation of competition in toll pricing on a network utilising two alternative algorithms. In the first algorithm, we utilise a Gauss Seidel fixed point approach based on...