Bertrand’s Paradox

I’ve been reading up on antitrust, and just came across Bertrand’s Paradox: that a market with two firms selling identical products will be competitive. It’s the starting point for trying to give a theory of cartels; you have to explain why the cartel members don’t fall into the trap of undercutting each other until they reach the competitive price. But as soon as I saw the name, I thought, Bertrand’s Paradox, isn’t that the one about the cartel consisting of all firms that aren’t part of a cartel?

(Bonus: There are actually three Bertrand’s Paradoxes, all named after the same guy. Not one is actually a paradox.)

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Why aren’t they paradoxes?

I also thought of Bertrand Russell’s paradox. Maybe Joseph Bertrand took some of its fame?

Hi James,

I too have sometimes confused Russell’s antimony and Bertrand’s paradox!

Bertrand’s probability paradox is fun. I teach it every year in honors 11th grade.

Also, Bertrand’s “Postulate” (same Bertrand, and much like these paradoxes are not paradoxes, this Postulate is not a postulate — it’s a Theorem) is fun to work through. It says that for n>1, there is always at least one prime between n and 2n. I have a nice, readable 1.5 page proof in pdf form (from a prof in Australia) should you (or anyone else) ever want to check it out.