Algorithm for equilibrium in the symmetric two-player Hirshleifer contests

In this work we study equilibrium points in the symmetric two-player Hirshleifer contests, which are going to be called Hirshleifer equilibrium point. We extend the Quasi-Newton method to the setting of this type of equilibrium point. The numerical algorithm is developed for multiobjective optimization problems based on the properties of Hirshleifer equilibrium point. Some preliminary numerical results are reported showing the performance of our algorithms.We present a possible way for converting single objective optimization to multiobjective optimization which is discussed in detail in our study.