0
$\begingroup$

generally it's true that Pure price of anarchy is >= mixed price of stability. but I just find cases where they are equal and I can't think of a case of strict inequality.

can you help me please?

thanks (: benny.

1 Answers 1

1

Consider the following two-player game $\begin{matrix}& L & R \\ T & 1,1 & 0,0\\ B & 0,0 & n,n\end{matrix}.$ The game has two Nash equilibria: $(T,L)$ and $(B,R)$; the price of stability is 1 (as $(B,R)$ is a socially optimal strategy), whereas the price of anarchy is $\frac{1}{n}$.