The final auction price calculated based on AMM
Last updated
Last updated
Assume these auction parameters:
Initial Pool: 10 ETH and 1,000,000 BID
Total Participants: 30
Price Multiplier: 4.9012 (calculated based on 30 participants)
Participants bid on their desired amount of BID units. Prices adjust dynamically based on demand, and refunds are given if bids are insufficient.
Example Participant Information
Participant
Bid (ETH)
Units Requested
1
1.56
10
2
4.93
3
The core of the AMM model is the constant product formula:
where:
To calculate the ETH needed for a specific BID purchase:
Determine the new BID balance in the pool after the purchase:
Use the constant kkk to find the new ETH balance:
Calculate the base ETH cost for the purchase:y\
Calculate Required BID Units and Base ETH Cost:
Participant 1 requests 100,000 BID (10 units at 10,000 BID each). The base ETH cost calculated using the AMM model is 1.11 ETH.
Participant 2 requests 30,000 BID (3 units). The AMM base cost for these units is 0.31 ETH.
Apply Price Multiplier:
Participant 1: 1.11 ETH * 4.9012 = 5.45 ETH
Participant 2: 0.31 ETH * 4.9012 = 1.51 ETH
Determine Auction Outcome:
Participant 1 bid 1.56 ETH, which is below the required 5.45 ETH, so they do not win and receive a full refund.
Participant 2 bid 4.93 ETH, which covers the 1.51 ETH needed, so they successfully purchased their 3 units. Their final cost is 1.51 ETH, and they receive a refund of 3.42 ETH.
Participant
Bid (ETH)
Units Requested
Successful Units
Cost (ETH)
Refund (ETH)
1
1.56
10
0
0.0
1.56
2
4.93
3
3
1.51
3.42
In this setup, the AMM model dynamically adjusts prices based on demand. Successful participants pay the AMM-adjusted price, while unsuccessful bids receive full refunds.
Total participants: 30
Final price multiplier: 4.9012
Total successful ETH spent: 9.8260 ETH
Total successful BID units purchased: 167
Average price per unit: 0.05883832 ETH
Total successful bids: 28
Participant
Bid (ETH)
Units Requested
Successful Units
Cost (ETH)
Refund (ETH)
1
1.56
10
10
0.4951
1.0649
2
2.93
3
3
0.1505
2.7795
3
1.65
5
5
0.2528
1.3972
4
0.36
5
5
0.2554
0.1046
5
0.33
8
0
0.0
0.33
6
3.36
2
2
0.1029
3.2571
7
2.59
2
2
0.1033
2.4867
8
1.82
4
4
0.2079
1.6121
9
2.41
9
9
0.4742
1.9358
10
4.44
9
9
0.4832
3.9568
11
0.95
4
4
0.2177
0.7323
12
2.63
6
6
0.33
2.3
13
1.07
8
8
0.4466
0.6234
14
3.07
9
9
0.5117
2.5583
15
1.22
9
9
0.5217
0.6983
16
3.72
6
6
0.3536
3.3664
17
3.07
2
2
0.1189
2.9511
18
4.77
2
2
0.1194
4.6506
19
3.74
10
10
0.6051
3.1349
20
1.49
9
9
0.5563
0.9337
21
4.42
4
4
0.2509
4.1691
22
3.91
8
8
0.5086
3.4014
23
0.32
8
0
0.0
0.32
24
2.64
4
4
0.2578
2.3822
25
3.99
7
7
0.457
3.533
26
4.11
9
9
0.5985
3.5115
27
4.19
9
9
0.6113
3.5787
28
0.83
1
1
0.0687
0.7613
29
4.95
6
6
0.4158
4.5342
30
4.49
5
5
0.3511
4.1389
is a constant (initially set as the product of initial ETH and BID in the pool).