I find all of this very exciting, especially the fact that you're keeping each mechanic very simple. The bidding war mechanic should be a lot of fun, although you'll need to determine whether to have a live auction (players take turns bidding until all pass and the low bid takes it), or a silent auction (players all place bids in secret, then reveal them at the same time, with some form of tiebreaker). I toyed with the ideas of both for my latest design, tried the silent auction variant, then decided to change some things up and got rid of bidding completely. For your game I think its a great fit though.
I had one idea that might help with a few of the issues you identified. Putting myself in the adventurer's shoes, I can think of very few dungeon crawl games where I was able to start out with a full set of gear, and in most games it will take some time to compile a full set. Perhaps each adventurer in your game could start with an item or two, and then be limited to buying a single item each time he or she comes to town.
For example, Quanthar the Barbarian walks into town with a sweet helm and a wielding a butter knife. He would then entertain offers for a breastplate, a shield, bracers, etc., or a better version of his current gear (probably a weapon, since his helm is sweet!) Any player could offer an item that Quanthar would be interested in buying, and the one with the best offer (as defined by your formula, or some other criteria that Quanthar uses to make decisions) would win the sale. After Quanthar buys his shiny new breast plate, the next time he comes to town, he's collected more gold from questing, and is looking for another piece of gear.
This would help limit the rate at which adventurer inventories fill up, and prolong the window in which low level blueprints would be valuable. This set up would place some restrictions on you when designing the criteria by which adventurers make buying decisions, but hopefully would help to set a slower pace for the game that will allow more chances for players who start slowly to win a few bids. If parties consist of 3+ adventurers, this would still allow for quite a bit of selling action each turn as well.
Happy designing!
I think silent auctions would be great. It would stop players from simply trying to continually out do each other by one (as would happen in an ordinary auction), but as for a tie breaker I'm not sure. Again, the nature system could work, but it seems kind of clunky. It would make sense that the player with the most fame could get the sale, but it would also give the player who is already winning another advantage, which could be unfair.
A good idea with having to buy a single item every time they are in town. One problem with this is that each party member has only 2 equipments (a weapon and armour), and there are 3 members in a party. Perhaps each party can only bye on piece of equipment? I've been thinking lately to possibly do away with the party system entirely, or change it though, so any feedback would be great. The bidding idea is great though just as you said, with each player bidding to sell the player new gear. Man, some great ideas over all here, and you gave me a good chuckle with the sweet helm! Bravo :)
One problem would be how they would be able to win in dungeons at the start though. It seems like at the beginning each dungeon would be quite hard, and after they got even 2 more pieces of gear, it would become twice as easy. The difficulty curve would be rather hard, especially if they start losing gear due to breaking as well. Possibly each party starts with 3 pieces of gear, and can buy 1 after every dungeon they're in? Maybe as you said, there could be more then 4 party members as well. Originally I had an idea for some general class guidelines in a party, so that you couldn't just sell any sort of gear to any member in a party. Each party would have a Warrior, Archer, and Mage, and this could limit each party to having 6 pieces of gear (2 for each specific class). I just personally though it would make the game more exciting to have some classic fantasy arch types thrown in, but I'm not entirely sure any more.