To help illustrate how this auction will work, 
I'll use a character of my own for an example.  
Suppose I wanted to play another version of Liam 
(who is known by the other characters as being mostly a Trump Artist).  
If I were to play Liam in this scenario, 
these are the Initial Bids that I might do.  


These would be his Initial Bids for Attributes, Powers, and "Stuff": 

Psyche:    25 points
Strength:   (no bid)
Endurance: 25 points
Warfare:   50 points

Pattern Imprint:  50 points
Logrus Mastery:    (no bid)
Trump Artistry:  100 points
Shape Shifting     (no bid)
Power Words:      15 points
Sorcery:          15 points
Conjuration:      20 points

"Stuff": 25 points

(Subtotal: 100 points for Attributes 
         + 200 points for Powers 
         +  25 points for "Stuff"    = 325 points spent so far)


Based on these Initial Bids for Attributes, Powers, and "Stuff", 
Liam would have the following modifiers for all of his bids on Positions and Items: 

Marshal of Arden:     +17   (STR + WAR =  0 + 50 = 50; 50 / 3 = 16.667)
Admiral of a Fleet:   +25   (END + WAR = 25 + 50 = 75; 75 / 3 = 25)
Captain of the Guard: +17   (STR + WAR =  0 + 50 = 50; 50 / 3 = 16.667)
Prince of Rebma:      +17   (PSY + END = 25 + 25 = 50; 50 / 3 = 16.667)

Possession of a Pattern-Sword:     +33   (WAR + Ptn =  50 +  50 = 100; 100 / 3 = 33.333)
Mastery of the Jewel of Judgement: +25   (PSY + Ptn =  25 +  50 =  75;  75 / 3 = 25; 
                                          Log + ShS =   0 +   0 =   0;   0 / 3 =  0; 
                                          total     =  25 -   0 =  25)
Possession of a legacy Trump Deck: -42   (PSY + Trm =  50 + 100 = 125; 125 / 3 = 41.667)

Note to "Math-Phobes": Don't panic!  
The GM (that's me :-) will compute your Modifiers for you.  
All you will have to do is simple addition (see below).  


Based on these Modifiers, and on the following Actual Bids, 
Liam would have the following Effective Bids 
for his Initial Bids on Positions and Items: 

Marshal of Arden:     (no bid)
Admiral of a Fleet:   (Actual Bid   = 15) 
                      Effective Bid = 40   (25 + 15 = 40)
Captain of the Guard: (no bid)
Prince of Rebma:      (no bid)

Possession of a Pattern-Sword:     (Actual Bid   = 50)
                                   Effective Bid = 83   (50 + 33 = 83)
Mastery of the Jewel of Judgement: (Actual Bid   = 10)
                                   Effective Bid = 35   (10 + 25 = 35)
Possession of a legacy Trump Deck: (no bid)

(Subtotal: an additional 75 points spent, for a running total of 400 points spent)


Thus, Liam's Initial Bids will look like this: 

Psyche:    25 points
Strength:   (no bid)
Endurance: 25 points
Warfare:   50 points

Pattern Imprint:  50 points
Logrus Mastery:    (no bid)
Trump Artistry:  100 points
Shape Shifting     (no bid)
Power Words:      15 points
Sorcery:          15 points
Conjuration:      20 points

"Stuff": 25 points

Marshal of Arden:             (no bid)
Admiral of a Fleet:   "40" (15) points
Captain of the Guard:         (no bid)
Prince of Rebma:              (no bid)

Possession of a Pattern-Sword:     "83" (50) points
Mastery of the Jewel of Judgement: "35" (10) points
Possession of a legacy Trump Deck:         (no bid)

Furthermore, as Liam has spent only 400 of his 500 points, 
he still has another 100 points to use in the Auction or later.