At the initial stage of the mainnet launch, Polkadot will serve as the first relay chain (Relaychain) to complete the verification and communication with other parachains (Parachain), then the interface connecting the Polkadot chain to the parachain is called a slot (Slot). The card slot refers to the interface between the relay chain and parachain/parallel thread, the interface between the relay chain and the bridge chain (Bridge) in the Polkadot network architecture.

The reason why Polkadot’s parachain card slots are very limited in the early days is that the parachain itself needs to consume network resources all the time. In the early days of the network. It is expected that there are about 10 validator nodes (Validator nodes) for each parachain, and more collator nodes (Collator nodes) are needed. The relay chain needs to maintain a shared security pool of multiple parachains, so it will not open too much in the early stage. Multiple slots out.

The card slot is like the socket of a home appliance socket, and the parallel chain is similar to electrical appliances with various functions. In the case of limited cable carrying capacity, only a few necessary household appliances can be "powered on".

According to agency news, from the limited opening of about 27-32 card slots at the beginning of the launch, to the entire version 1.0 (the span of about 2 years from the launch of the mainnet) will eventually have about 80 card slots available for competition (except about 10 slots are pre-allocated). About 80 card slots will be allocated to parachains within 2 years; a certain proportion of card slots will be allocated to parallel threads (parathread) and bridge chains (bridge).

Projects connected to the Polkadot mainnet will compete for parachain card slots in the form of candle auctions. The auction adopts the candle auction method (CandleAuction), which means that the auction will stop immediately at a certain point in time (candles are in At the end of the combustion, the wick falls or goes out at a certain point, and the auction stops immediately (hereinafter referred to as "fuse"), and the bidder with the highest bid wins.

In the case of candle auctions with the same candle mechanism, the time at which the auction stops has a normal distribution of the probability of a circuit breaker based on the "structure of candle settings". Here is a candle that will melt when there is a high probability of 2-4cm remaining in reality as a display.

According to the research literature of the Web3 Foundation, the candle auction design of the Polkadot parachain is to hope that the bidder with a higher valuation in mind has a higher chance of winning the bid, which is related to the difference between its valuation and the market's valuation. A retroactive close means that bidders need to submit their bids carefully after the auction starts.

According to the research literature of the Web3 Foundation, it is assumed that the auctioneer (P) evaluates the bidding card slot as V; the highest valuation among all other auctioneers, referred to as the market valuation is; the bidding price is b; we then set α∈(0,1 ] is the random % of the next bidding increase.

when b

Under the traditional auction mechanism where the highest bidder wins, the probability of successful bidding Pr[P iswinning] will tend to an infinitely high probability as the bidding price increases.

However, under the candle auction mechanism, with the same valuation (V) and the same bidder (P), the final auction price will be randomly distributed among the expected prices V according to the random candle blowout.

($40-$100-$140 is the weight of a card slot valuation V)

Therefore, if and only ifHere we assume: Vmax full market valuation = $100 = set as the valuation weight of a card slot. (see bottom column of table above)

The bid increase is 10%, then the last successful bidder bids

Must be greater than market valuation. It is preliminarily calculated that bidders generally need to prepare funds higher than the market valuation in order to succeed in the candle auction.

Then, in the case of random number valuation V and increase, we set the total number of auction rounds to be n, and one of the rounds of the total number of rounds set by the system will randomly perform candle melting, which is set as the firstRounds. According to Parity's setting of the bidding procedure, if the bidding price b

The total number of bidding rounds here is n, which is counted as the nth block (the total length of the candle wick), but the auction will most likely be terminated at the block before the nth block. Under normal circumstances, bidder P needs to have a higher valuation V than other bidders:In order to win the auction at the random closing time (n-1/αth block).

The difference between bidders' estimates is therefore:, and the additional funds (additional costs) that successful bidders need to prepare are:

Assuming that the market valuation of the whole site (except bidder P) is $100, and the bid increase is 10%, then the final additional cost =, it can be concluded that in the case of advancing the rounds, the success rate decreases and the additional cost increases, and the bid of the bidder P must beThere is a chance that the auction will be successful.

In order to study the relationship between bidding increase and additional cost, we assume that the bidder P's valuation V==$100, in the total roundUnder the premise, assuming n=10, then there are