Some applications of Berge's theorem to equilibrium problems

This work surveys two theorems of the existence of solutions to equilibrium problems by applying Berge's maximum theorem [5] and Kakutani's fixed point theorem [9]. The first theorem is an alternative statement of Debreu's social equilibrium existence [6], and the second is an extension of the competitive equilibrium result that shows Nash-Walras equilibria existence, assuming interdependent and price-dependent preferences. Both theorems extend the classical results of the existence of Nash equilibrium [10] and competitive equilibrium [2], respectively.