Chapter 15 Existence of competitive equilibrium This chapter discusses that the mathematical model of a competitive economy conceived as an attempt to explain the state of equilibrium reached by a large number of small agents interacting through markets. Four distinct but closely related approaches to the existence problem are recognized. At first proofs of existence of an economic equilibrium were uniformly obtained by application of a fixed point theorem of the Brouwer type or Kakutani type or by analogous arguments. This approach which has remained of central importance to the present is the subject of the chapter. Second in the past decade efficient algorithms of a combinatorial nature for the computation of an approximate economic equilibrium were developed. Third recently the theory of the fixed point index of a map and the degree theory of maps were used to establish the existence of an economic equilibrium and finally a differential process was proposed whose generic convergence to an economic equilibrium provides an alternative constructive solution of the existence problem.