How robust are economic models to the introduction of irrational agents? The Pareto efficiency of competitive equilibria is not robust since one irrational agent leads to inefficiency. But the property that rational agents cannot use their own resources to Pareto improve on their competitive allocation holds regardless of the number of irrational agents. Full production efficiency can be robust as well, but irrational firms introduce a trade‐off between efficiency and the attainment of Pareto improvements. Regarding games, I show that while existing implementation mechanisms are sensitive to the presence of irrational agents, there are robust alternatives with attractive welfare properties.