When you state that you would prefer having the console than being paid for it, I imagine you mean you'd prefer having it than being paid your share of the current market price. Despite what game data is on the console, there is surely some price at which you are happy to part ways with it. Both of you seem like you would be happy to buy each other's half for $175, but not sell it for that much.
Suppose you and your former roommate with his new roommate both bid on your respective halves of the console. Each of you have some sort of reservation price, the highest price you'd be willing to pay to get the other person's half of the console, which will be above $175. (Likewise, it'd be the minimum you'd need to receive to part with your half, if both "halves" are homogeneous.) It's true that your former roommate will have someone else helping him pay, but that should not be a problem for you as long as you are not constrained by your budget and have to bid strategically. That is, if your budget is greater than your reservation price, you'll be fine.
There are two straightforward mechanisms I could suggest.
- Both parties enter a sealed bid (your former roommate and his friend can determine their own cost sharing rule). Whoever bids highest wins, but pays the amount the other person wrote down. This is effectively a second price auction, which normally prevents strategic bidding, but as denesp notes, payoffs do depend on your own bid.
This method's split is not equitable. One person will end up getting exactly what they would need to part with their half (again, assuming both "halves" of the console are identical).
- Both parties enter a sealed bid. Highest bid wins, and you split the difference between the two bids and pay that. So if you bid 250 and your friend bids 220, then you win, and end up paying your friend 235. This has a little more room for finagling around with strategic bidding, but the max-min strategy is to also bid your reservation price. If you underbid and lose, then you might get less money than you would want for having to part with your half. So there is some protection here.
This method is equitable, but again, a little more prone to strategy.
Take those suggestions for what they are worth. I think they are relatively easy to implement, so maybe there is something more efficient, but eh.