This shouldn't be surprising to anyone who knows that Kakutani/Brouwer's fixed-point theorem (the basis of Nash's formulation of game theory and General Equilib

This shouldn't be surprising to anyone who knows that Kakutani/Brouwer's fixed-point theorem (the basis of Nash's formulation of game theory and General Equilibrium Theory in neoclassical economics) was proved non-constructively. It assumes that there's a continuous endomorphism in a convex space with no fixed points, and shows that you can use such a function to retract to the boundary of that space [1][2]. However, the boundary itself is full of fixed points, and this shows by contradiction that fixed points must exist for continuous endomorphisms. By presuming the non-existence of the fixed points in such a proof, you can't use it to arrive at any fixed point. Nash uses a clever argument to show these fixed-point equilibrium strategies exist in games, and Debreu and Arrow use a similar argument in the space of preferences to find equilibrium prices. [3] Unfortunately, these theories have been used to promote the myth that markets are self-regulating despite all evidence to the contrary. [4][5] [1] Lawvere - Conceptual Mathematics [2] https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem#A_proof_using_homology https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem#A_... [3] https://en.wikipedia.org/wiki/Arrow%E2%80%93Debreu_model https://en.wikipedia.org/wiki/Arrow%E2%80%93Debreu_model [4] http://coin.wne.uw.edu.pl/mbrzezinski/teaching/HE4/BlaugFormalistRevolution.pdf http://coin.wne.uw.edu.pl/mbrzezinski/teaching/HE4/BlaugForm... [5] Weintraub. Stabilizing Dynamics: Constructing Economic Knowledge