The Auction Market is where investors such you and me, as well as Market Makers, buy and sell securities. The Auction Markets operate with the familiar bid-ask pricing that you see on financial pages such as Google and Yahoo. The Market Makers are institutions that are there to provide liquidity so that investors can easily buy and sell shares at a "fair" price. Market Makers need to have on hand a suitable supply of shares to meet investor demands. When Market Makers feel the need to either increase or decrease their supply of a particular security quickly, they turn to the Dealer Market.
In order to participate in a Dealer Market, you must be designated a Market Maker. As noted already, Market Makers are dedicated to providing liquidity for the Auction Market in certain securities and therefore require that they have on hand a suitable supply of those securities which they support. For example, if a Market Maker for Apple shares is low on their supply of Apple shares, then will go the Dealer Market to purchase more Apple shares. Conversely, if they are holding what they feel are too many Apple shares, they will go to the Dealer Market to sell Apple shares. The Dealer Market does operate on a bid-ask basis, contrary to your stated understanding.
The bid-ask prices quoted on the Dealer Market are more or less identical to those on the Auction Market, except the quote sizes will be generally much larger. This is the case because otherwise, why would a Market Maker offer to sell shares to another Market Maker at a price well below what they could themselves sell them for in the Auction Market. (And similarly with buy orders.) If Market Makers are generally holding low quantities of a particular security, this will drive up the price in both the Dealer Market and the Auction Market. Similarly, if Market Makers are generally holding too much of a particular security, this may drive down prices on both the Auction Market and the Dealer Market.
