Specifications of the auction market

Some features of our synchronous double auction is summarized in Table 1.

 

 

Table 1: The difference between our synchronous double auction and some other synchronous double auctions

Our auction	Other synchronous double auctions
1. Each agent submits both buy bid and sell bid;	An agent can only submits either bid or sell bid;
2. Multiple trading price at each period;	One central trading price;
3. One type of k-double auction with k=1/2.	May not be a k-double auction.

are The auction process can described as the following: At the start of the auction, each agent is endowed with designated amounts of m goods, each--except the last--associated with an auction. Each time period constitutes a bidding round for one auction, rotated in turn. Agents bid in an auction by posting buy and sell prices for one unit of the good j. All prices are expressed in units of good m.

  

Figure 1: Bidding and trading in the synchronous double auction

After all agents submit their bids, the auction matches the highest buyer to the lowest seller, if the buy price is greater than the sell price. The trading price for the match is equal to $\frac{1}{2}P^{buy}+\frac{1}{2}P^{sell}$, where P^buy is the price offered by the buyer, P^sell is the price offered by the seller. The auction then matches the second highest buyer with the second lowest seller, and so on, until the highest remaining buyer is offering a lower price than the lowest remaining seller. At this point, the market proceeds in turn to the next auction. In the new round, agents post their buy and sell prices for the next good, and they are matched according to the prices they post. The market continues until no agents can be matched in any auction. Figure 1 shows the matching process in one period of an auction.