Comments on: The Non-Mathematical Guide to Fixed Point Theorems and Proving Nash Equilibria Exist

By: The ‘magic’ number 495 - Mind Your Decisions

The ‘magic’ number 495 - Mind Your Decisions — Tue, 11 Oct 2011 05:06:04 +0000

[...] Fixed points are a useful mathematical entity, and they have a special place in game theory. The way John Nash proved that many games have equilibria is by using a fixed point theorem: he showed that under certain conditions, there must exist a set of strategies such that no player can deviate profitably. The set of strategies is a fixed point that survives the strategic thinking of every player responding to the other players. (more on that here) [...]

By: The Dice Brain Teaser: A Technical Interview Question that Can Help You Solve Problems Better - Mind Your Decisions

Wed, 10 Aug 2011 04:41:18 +0000

[...] puzzle is special. I like it even more than previous brain teasers I’ve discussed, like the monk problem and the hat [...]

By: Game Theory scene from A Beautiful Mind - Mind Your Decisions

Game Theory scene from A Beautiful Mind - Mind Your Decisions — Wed, 10 Aug 2011 04:15:14 +0000

[...] A Nash equilibrium is a state where no one person can improve, given what others are doing. This means you are picking the best possible action in response to others–the formal term is you are picking a best response. (For more, see my article on why Nash equilibrium exist). [...]

By: The Ultimatum Game and The Hollywood Writer’s Strike - Mind Your Decisions

The Ultimatum Game and The Hollywood Writer’s Strike - Mind Your Decisions — Wed, 10 Aug 2011 03:45:35 +0000

[...] A Nash equilibrium is based on your beliefs about other players, and how accurate those beliefs are. I gave some intuition about the Nash equilibrium in this post. [...]

By: Presh Talwalkar

Presh Talwalkar — Fri, 31 Dec 2010 01:52:03 +0000

Thanks for the comment. Yeah, perhaps the soda can example is a bad one. Imagine instead you were rolling the soda can on the ground so it would explode. I think that would be continuous and Brouwer’s theorem would apply.