The Gjerstad Dickhaut (GD) Auction Strategy

1
The Gjerstad Dickhaut (GD) Auction Strategy

• as presented in the paper
• Price Formation in Double Auctions
• by Steven Gjerstad and John Dickhaut
• Presented by Marek Marcinkiewicz

2
GD The main idea

• Use previous bids to determine the probability
  that future bids will be accepted
• Combine this probability with profit to estimate
  how to place bids to maximize expected profit

3
History

• The algorithm requires previous bids made by all
  traders
• Since the agent has limited memory, a memory
  length L is specified
• L last trades and any shouts between them are
  stored

4
Frequency of Takes

• If there were many bids made at each price point
  than the probability could simply be the number
  of shouts accepted at a particular price point
• In a more likely sparse market this is not
  possible though since there are few bids
• But not only bids at some price point provide
  information to us

5
What do bids reveal?

• TBL taken bids lower than some price would also
  be taken at this price
• AL asks lower than some price would match a bid
  at this price
• RBG rejected bids greater than some price make
  it less likely that this price will be accepted
  because if they are rejected then why take this
  even lower offer?

6
Probability of bid

• P(b) TBL(b) AL(b)
• -------------------------------
• TBL(b) AL(b) RBG(b)

7
Spread reduction rule

• All bids must be higher than the last outstanding
  bid and all asks must be lower than last
  outstanding ask
• Minimum price is 0
• Maximum price is M (a value that nobody is
  willing to pay)

8
Interpolation

• Since probability is only defined at shout points
  that where already made, we have to interpolate
  these into the real space
• P(bk) calculated P(bk)
• P(bk1) calculated P (bk1)
• P(bk) 0
• P(bk1) 0

9
Interpolated Probability

• P(b) a3b3 a2b2 a1b1 a0
• Use previous 4 equations to solve for a.

10
Expected Profit

• Bid max(p(b) (b private value))
• Use the same type of strategy for asks