I am trying to understand how Nash Equilibrium works in the Gambit software but I can't figure it out. I have created a simple game shown below and I have calculated just one Nash equilibrium by tracing logit equilibria. Can someone explain to me what the numbers mean and what am I supposed to understand by them?
I don't know this software, but I'd guess it means:
Player $1$ (red) makes a move with options $1$ and $2$, and then Player $2$ (blue) makes a move, also with options $1$ and $2$; the tree corresponds to those options, the red numbers to the right of it are the corresponding payoffs for Player $1$ and the blue numbers to the right of them are the corresponding payoffs for Player $2$.
There's a single pure Nash equilibrium: Player $1$ plays $1$, if Player $1$ plays $1$ Player $2$ plays $2$ and if Player $1$ plays $2$ Player $2$ also plays $2$. The numbers in row "$1$" are the probabilities for the mixed strategy profile corresponding to this pure strategy profile.
The labels in the row "#" are a bit confusing, since they don't correspond to the labels in the game tree. In the game tree, $x:y$ means the $y$-th node at which Player $x$ plays; in the row "#", $x:y$ means the probability for the player to play option $y$ at node $x$, and which player this is is indicated by the colours in row "$1$".