This is an idea based on the framework for alternative auction systems outlined above, in combination with the 'packages' concept that John Biles developed primarily for his Unicorn no Senshi campaign. In some respects it turns the auction completely inside out from how the original system works. Rather than bid exclusively on attributes, with perhaps a limited number of items, then building the rest of the character's powers and skills with the remaining points, the Integrated auction works by bidding on various packages, which define what skills and powers the character has access to, and provides the baseline for attributes.
Every character starts with the same basic package
All skills and powers, as well as improvements to the baseline attributes, come from winning the various packages available for auction. The Integrated Auction system works best in campaigns using a partial power system and some variant of a skills and talents system. Since the majority of character "advancement" happens through the winning of these auctions, players should anticipate spending the majority of their points in the auctions.
Some auction packages are just like those in any other game, including many variants of the ideas listed about in the Alternative Auctions sections. However, the difference in an Integrated Auction is the presence of multiple training and career type packages. For example, a typical career package might be as follows:
Similarly a training package might looks like this:
Some packages will be clearly worth more than others. Many packages will be available more than once (see Vickery and Dutch auctions above for how this can work, along with the comments in Reserves and Buyouts). For example, Fiona could easily have more than one student, and in the course of centuries there could be more than one Captain of the Guards, and some truly generic packages could easly be had by all the players if they desire (infantry soldier, for example).
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Once all the auctions are held, the players can total up their stats, skills, and powers, use whatever points they have left to round out their character. The details of how this happens, like the individual packages available in the auctions, will be somewhat specific to each campaign. For example, some GMs will place a cap on the total number of additional points that can be placed in attributes, or specify a certain number that can be moved to make the character more to the liking of the player. Similarly, depending on how powers are to be purchased, it may be the case that the various packages have only given the opportunity to buy various powers, rather than being worth points towards the powers.
Here's an example of the Integrated Auction.
Here's a suggestion for an auction that is in someways a step both forward an back from a non-Attribute auction. The characters start with Amber in every level and access to no powers, and each auction item, in addition to the item itself, carries the possibility of gaining attribute points and powers. For example, Training with Fiona might grant 15 points of Psyche, in addition to the ability to get Sorcery or Advanced Pattern, plus getting several points worth of 'Fiona as ally'. The winner of 'Captain of the Guard' gets 5 points of Warfare, and 3 each of Endurance and Strength, due to the daily training and drilling. And so on. If the campaign is using one of the variants of the Notable Skills and Talents systems, auctions might also provide these as well. Even items and other non-obvious auctions could grant small bonuses to various attributes, particularly if you're using the sort of flavor text mentioned above, consider: "During the race to the spikard, you got into sevral fist fights and were severely battered several times, but came out stronger and tougher because of it." The runner-up could gain lesser improvements, as a further incentive to bid.
Further, this could be auction packages which are strictly designed to give attributes, such as 'Posting in the Amber Honor Guard', which conveys Warfare and Endurance, plus court ettiquette skills. Such auctions might not be exclusive wins, either, the top two or three bidders might gain the benefits, or as above, the runners-up could gain lesser versions of the benefits. Vickery auctions could also work, where there are a fixed number of positions, and the top bidders get them, at the cost paid by the lowest winning bid (if the top bids for a 2 slot Vickery auction were 4, 8 and 10, both the bidders for 8 and 10 would get the benefits, for a cost of 8 points).
Once all the auctions are over, and the attributes tallied, the players might have the option to adjust the stats more to their liking. For example, everyone gets a flat 10 points to spend as they want. Or can spend up to 10 of their remaining points (that would otherwise be spent on powers, non-unique items, etc). Or may rearrange 20 points among the attributes they have. Or perhaps increase or decrease each attribute a certain fixed amount (5 or 10 points) or a percentage (10% or 20%, perhaps), spending or regaining character points appropriately.
The end result of this sort of system is that the characters are much more "organic" in nature. They start with a degree of history, with attributes that tend to appropriately support the skills and powers they've been trained in. This sort of setup works best for games where the characters start relatively established, if younger, rather than those where the PCs start unaware of their natures, though with some careful tailoring of the various "stories" that go with each auction, it could still be done.