0
votes
1answer
62 views

Simulating Mixed Nash Equilibria

I have a $N$ person game where each person has a set of $M$ discrete strategies. I know from the theory that at least one mixed strategy Nash Equilibrium exists. Can someone please tell me how do I ...
4
votes
0answers
131 views

algebraic or homotopical proof for Kakutani fixed point theorem

As Kakutani fixed point theorem is a genral case of Brouwer fixed point theorem, and one can read the proof from homotopy theory books. I wonder if there is any proof for the Kakutani using homotopy ...
1
vote
2answers
542 views

Finding the fixed point of a function

Let $p:A \times B \to \mathbb{R}$ be a nonnegative real-valued function on $A \times B$, where $A$ and $B$ are arbitrary set. Assume $f:A \to B$ and $g:B \to A$ are such that \begin{align*} f(a) ...
8
votes
1answer
342 views

Common knowledge as a fixed point

I read on a wikipedia page that from the modal logic formalization CK can be formulated as a fixed point. If it also holds for the set theory formalization? If it does, where I can find about it? ...