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you can see the topic about the variant here:
https://boardgamegeek.com/article/27877079#27877079
but in short:
make 1 pile per player with 2 corps + 10 cards.
players bid on a pile, amun-re style. the bids values are 1,3,6,10,15,21,28,36 (guess that is enough? 
In order each player bids whatever they wish on a pile, then the next player can bid on a new pile, or if they want, overbid the first player.
When it comes to your turn, if someone took your spot you have to place a new bid, if not you cant do anything
The auction ends when all piles have a bid from someone (at least the last bid will be for 0
Then the payment can be made to the bank, but to avoid the game starting with lower $ you can average the bids, and give that to each player after they pay the bids
So bidding 10-4-2-0, average = 4 per player, so the actual payment would be 6 - 0 - receive 2, receive 4
Lets use the hands from a recent PBF game:
https://boardgamegeek.com/article/27877071#27877071
That I will copy below (only 4 to simulate a 4p game)
Pile A
InterplanetaryCinematics
Credicor
53 Lake Marineris
60 Trees
77 Solar Wind Power
99 Toll Station
104 Ore Processor
150 Anti-Gravity Technology
152 Insulation
159 Lichen
165 Magnetic Field Generators
201 Energy Tapping
Pile B
TharsisRepublic
Teractor
27 interstallar colony ship
125 hackers
46 lightning harvest
33 regolith eaters
160 power supply consortium
88 heather
194 power infrastructor
62 mineral deposit
192 invention contest
182 corporate stronghold
Pile C
UNMI
PhobLog
162 imported GHG
55 kelp farming
195 indentured worker
37 nitrogen rich asteroid
66 land claim
178 heat trappers
96 green houses
24 predators
164 micro mills
167 import of advance ghg
Pile D
Ecoline
Thorgate
156 standard technology
119 dust seals
21 phobos haven
205 rad chem factory
149 CEO's favorite project
91 gene repair
111 business contacts
59 mangrove
11 big asteroid
72 birds
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I'll start, we can use this format
A - no bid yet
B - no bid yet
C - no bid yet
D - Pedro bids 10
(so X can bid
A - X bid 6
B - no bid yet
C - no bid yet
D - Pedro bids 10
or
A - no bid yet
B - no bid yet
C - no bid yet
D - Pedro bids 10 - X overbids 15
I should then remove my "Pedro bids 10" when its my turn and I have to bid again on something else or overbid again 
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So, cant we find 3 players to give it a go?
We dont even have to all meetup and actually play the game that this would set up xD
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