What is equilibrium dependent upon in Generalized Second-Price Auctions?
The surplus is the value of the object obtained minus the price paid. In your first example, the surplus would be $10-7 = 3$. The reason why you don't find examples where BOTH players are not using optimal strategies is because $b=v$ is weakly dominant. Unlike a lot of games where you need to consider best response functions, this one can be solved simply by removing dominated strategies.

Using your first example, there exists no bids that will give a higher payoff than $b_i=10$ regardless of what $b_{-i}$. Suppose we look at player 1, then consider all cases:

$b_2 &lt; b_1 &lt; v_1$: surplus is the same as $b_1=v_1$ 

$b_1 &lt; b_2 &lt; v_1$: surplus is 0, $b_1=v_1$ is profitable deviation

$b_1 &lt; v_1 &lt; b_2$: surplus is the same as $b_1=v_1$ 

$v_1 &lt; b_1$ surplus is negative or 0 (depending on $b_2$), $b_1=v_1$ is profitable deviation 

Also, auctions are usually used for a non dividable object, which means that examples with multiple players with the same value require a tie breaking rule. Whether or not this weak dominance survives depends on this tie breaking rule.