Nash equilibrium in second price sealed-bid auction I'm trying to understand the basics of game theory and the topic of auctions has arisen. I understand the basic concepts of auctions but I'm struggling with second price sealed-bid auctions.

I understand that a weakly dominant strategy in a second price sealed-bid auction is to always bid the amount how much the item is worth to you. However I'm having trouble with some example questions that I've been given.

We have $n$ bidders, $n \ge 2$. There is only one object in the auction. Player $i, i = 1, . . . , n,$ evaluates the object by giving it a valuation $v_i$ , where:

$$v_1 &gt; v_2 &gt; v_3 &gt; . . . &gt; v_n &gt; 0$$

Each player i submits a sealed bid $b_i \ , i = 1, . . . , n$. So, we can describe a bidding profile of all players as $(b_1, b_2, b_3, . . . , b_n)$.

Now what I what I want to understand is are both the listed bidding profiles below nash equilibrium? 

A) bidding profile  $(v_1, 0, 0, . . . , 0)$

B) bidding profile $(v_2, v_1, 0, . . . , 0)$ 

Surely both are a nash equilibrium because every bidder will bid there valuation for the item thus no one has any incentive to change there bid? E.G a weakly dominant strategy

I just wanted some clarification, any help on the matter would be greatly appreciated.
In scenario $A$, only the highest bidder bids their true value and everyone else bids $0$. None of the other players can increase their payoff by changing their strategy alone, as no one values the item above $v_1$. This makes it a weakly dominant strategy.

In scenario $B$, the bidder valuing the item at $v_1$ bids $v_2$ and the bidder valuing the item at $v_2$ bids $v_1$, with $v_1 &gt; v_2$. In this scenario, Player 2 is actually bidding $v_1 - v_2$ above their true value, making it beneficial for this player alone to switch to bidding lower than $v_2$ to obtain $0$ value instead of his current negative value. Thus this is not a weakly dominant strategy.
In scenario $A$, only the highest bidder bids their true value and everyone else bids $0$. None of the other players can increase their payoff by changing their strategy alone, as no one values the item above $v_1$. This makes it a weakly dominant strategy.

In scenario $B$, the bidder valuing the item at $v_1$ bids $v_2$ and the bidder valuing the item at $v_2$ bids $v_1$, with $v_1 &gt; v_2$. In this scenario, Player 2 is actually bidding $v_1 - v_2$ above their true value, making it beneficial for this player alone to switch to bidding lower than $v_2$ to obtain $0$ value instead of his current negative value. Thus this is not a weakly dominant strategy.