Chapter 14. The Complexity of Computing Equilibria In one of the most influential existence theorems in mathematics John F. Nash proved in 1950 that any normal form game has an equilibrium. More than five decades later it was shown that the computational task of finding such an equilibrium is intractable that is unlikely to be carried out within any feasible time limits for large enough games. This chapter develops the necessary background and formalism from the theory of algorithms and complexity developed in computer science in order to understand this result its context its proof and its implications.