How to auction shared item with a roommate? My roommate and I split the cost of a game console a year ago (~$400) but he is now moving out.

We were wondering how to fairly auction the console given the situation:


We both paid an equal price of $200+
Right now half the market price of the console is \$175
We both would prefer having the console than being paid for it
He will be splitting the price with his new roommate whereas I will be paying by myself


With regular bidding, as my roommate representing both him and his next roommate and me myself, is he at an advantage because he has double the market power? If yes, how can we fix that problem?

Outcome:

Thank you for your answers. While the chosen answer seemed the best way to do this, we both felt it involved too much strategy and would have resulted in envy from one of us. We instead went with the Divide and Choose method, which worked out fairly for both of us.
If you think that the distribution of your value and your roommate's value are the same then I would suggest that you consider the following bidding protocol:


each bidder submits a sealed bid, $b_i$.
the highest bidder, $i$, received the console and makes a payment of $\frac{b_i+b_j}{2}$ to the loser, where $b_j$ is the loser's bid.


Cramton, Gibbons, and Klemperer (Econometrica, 1987; Section 4) show that this is an efficient way to dissolve a partnership with joint ownership stakes in an asset.

If you think that the two of you have differing value distributions (e.g. because your roommate has a new friend) then Cramton et al. show in Theorem 2 how to adjust the pricing rule to restore efficiency. 

I highly recommend taking a look at the Cramton et al. paper. It's surprisingly readable for an Econometrica.

Let us know how you get on if you decide to try it out!