[neel_k]

Sure it can.

Actual competitive markets are made of competing firms, and firms can't (in general) optimise.

1. Holmstrom's theorem tells us that no payment system for a team of agents can have a budget in balance, be in Nash equilibrium, and be Pareto efficient.

2. Since firms are definitionally teams of people, and since you don't get a choice whether the budget balancing or the workers optimise, this means that firms must sacrifice Pareto efficiency.

3. If firms can't always seek out the Pareto frontier, then a competitive market composed of firms will not satisfy the conditions for Walras' theorem to hold, and so competitive markets can't necessarily reach equilibrium.

[alisonkisk]

Holmatrom theorem can have a budget surplus, With Nash Equilibrium and Pareto efficiency. Businesses are (ideally) run with a budget surplus, with profit extracted.