Fisher market

Assume the quantities are normalized so that there is 1 unit per product, and the budgets are normalized so that their sum is 1. Also assume that all products are good, i.e., an agent always strictly prefers to have more of each product, if he can afford it.

While Sperner's lemma can be used to find a CE, it is very inefficient computationally. There are more efficient methods: see Market equilibrium computation.

When the items in the market are indivisible, a CE is not guaranteed to exist. Deciding whether a CE exist is a computationally hard problem.