Brown Bears Bidding on Honey

Question

I'm dealing with a problem where Brown Bears are bidding on a pot of honey. Imagine that we have $n$ Brown Bears $B_1,B_2,...,B_n,$ and brown bear $B_i$ values the honey pot $v_i \in \mathbb{R}^{+}.$ Consider a bidding structure where each brown bear $B_i$ submits a bid $b_i \in \mathbb{R}^{+}\cup\{0\}$, and then the person with the second highest bid wins the auction and pays the fourth highest bid. Anyone who doesn't win does not pay a bid. Imagine that the payoff for bear $B_i$ is $v_i-b_i$ if bear $B_i$ wins and $0$ if bear $B_i$ loses. I want to figure out what is the optimal strategy for each bear. Is it possible that I should be using the revenue equivalence theorem in this scenario? Otherwise, I am not sure what theorems to potentially use here.