"Compared with the English auction, our auction format (candle auction) will have two major differences: (1) first, the candle auction will have an approximate closing time range, (2) and allow each Bidders' pricing can be made public or choose not to.
fairness
fairness
Fairness here means that in a candle auction mechanism, buyers with higher bids will have a higher winning rate than other auctioneers, so that in an auction mechanism where the auction time ends randomly, the highest bid among all auctioneers More people can win the bid, and the higher bid winning rate can be estimated from the difference in bids.
A random closing time, simulating the actual candle auction candle, when the candle blows randomly, it means the auction is over. Therefore, a random closing time also means that bidders should be careful to submit their bids and submit them before the roughly estimated end time of the auction. This mechanism also prevents sniping in the auction.
Otherwise, the random ending auction mechanism will not harm the fairness of auctioneers who do not make their bids public. For a completely open and transparent auction process on smart contracts, it is relatively fair to use candle auctions. In such a condition where the auction ends randomly and the auctioneer carefully submits the bid, the person who maliciously sabotages the auction also needs to bear the high cost risk. Griefing refers to bidding above the estimate to force the winner to pay more.
We want to present a smart contract strategy where, when rationally assumed, no one bids more than their own maximum valuation. In the case of using Epsilon equilibrium (also known as: approximate Nash equilibrium, refer to "Algorithmic Game Theory"), almost dominant game strategies can satisfy the existence of Nash equilibrium points within certain well-defined ε (Epsilon) factors. We track that bids above estimate (i.e. with the intent to sabotage the auction) create a risk of loss for those bidders.
Bidding strategy on smart contracts
We want to find a strategy that minimizes the disadvantages of smart contracts compared to bidding mechanisms with closed auctions (tender system).
Let's assume we have a bidder with a bid price (valuation) for an auction item, i.e. a parachain slot. We set a to be the price increase and want to find a
Formulate the strategy Sp bidder P as follows. If the following two conditions are met:
In the last block P did not win,
For the winning bid, b, the last block b
Then in the next block P bids for b+aV
If the following two conditions are met:
n is the number of blocks, and also represents the total number of auction rounds
The alpha markup is chosen as a trade-off between avoiding overpayments and increasing the chance of winning. When the number of bidding rounds n is relatively large, the price increase range a can be small, and when the total number of auction rounds n is relatively small, the price increase range a needs to be large. Larger alpha markups increase the chances of winning, but may result in unnecessary overpayments for the winner. Next, we first describe the winning chance and utility of the smart contract, and then use the total number of blocks to calculate the markup α to evaluate the last block P, and the highest estimated price of all other bidders.
odds of winning
Set: When there are at most 1/a-1 blocks, it represents the total number of rounds of bidding.
P didn't win,
b
Assuming there are n blocks in total, we want to calculate the probability that P wins when the following conditions are met:
If no one bids on their own bid
Other maximum bids and bids less than P
bids less than P
P wins with probability at least as follows:
where (1/a -1) is the probability that P will not win the auction. If V(1-a)>Vmax, then P will win with higher probability.
Program Design for Any Bidder
Now, let's assume P wins. How much does it cost? What is its utility?
Once P wins the bid in the auction, its utility refers to the amount saved by the bidder compared with the real value of the current Boaudi. The utility is defined as follows.If P wins the bid, the utility is aV
where b is the winning bid price in the block at the end of the auction. The most that P has to pay is Vmax+aV. The expected saving of P is at least equal to the probability of P winning multiplied by the maximum cost P pays.
We compare the expected utility with V-Vmax, which is the maximum result that guarantees utility P against other auction strategies. We need to differentiate between the two to find
to ensure that the winning bidder can at least save the auctioneer a certain amount of unnecessary expenses.
Next, we will look for Nash equilibria.
Compiled by: Shawn PolkaBase
