Generally speaking, when two parties wish to engage in a trade, the purchaser will announce the highest price he is willing to pay (the bid price) and seller will announce the lowest price he is willing to accept (the ask price).
The main advantage of such methods is that conditions are laid out in advance and transactions can proceed with no further permission or authorization from any participant. When any bid and ask pair are compatible, a transaction occurs, in most cases automatically.
When trading in a stock market, a person who has shares to sell may not wish to sell them at the current market price (quote). Likewise, a person who wishes to buy shares may not wish to pay the current market price either. Some negotiation is necessary in order for a transaction to occur.
The negotiation often comes in the form of adjusting the bid prices and the ask prices as the value of the share goes up and down. For example, if the share is worth $10, a buyer may "bid" $9.97 (3 cents less), and a seller may ask for $10.02 (2 cents more). If the value of the stock goes down, a seller may be forced to reduce his asking price. Conversely, if the value of the stock goes up, a buyer may be forced to increase his bidding price.
Most of the time, the bid and ask prices remain very close to the market value of the share, often separated by only a couple of cents. The difference between the bid and ask price is called the Bid/ask spread.
In actual trading, the parties involved might use a limit order to specify which bid or ask price he wishes to trade at. The trader specifies the number of shares and his bid/ask price (depending on whether he is buying or selling). Such orders can have execution limits, such as "by end of day" or "all or nothing".
An auction is a price mechanism where bidders can make competing offers for a good. The minimum bid may or may not be set by the seller, who may choose to predetermine an ask price. The highest bidder, or the first one to reach a preset ask price, would be awarded the transaction.
If the terms "pay" and "sell" are understood very generally, then, a very broad range of applications and different market systems can be enabled this way. Internet dating for instance could be based on offers to talk for a period of time, accepted by those who are compensated not in money but in additional credits to keep using the system. Or, a political party could trade support for different measures in a platform, perhaps using allocation voting to "bid" a certain amount of support for a measure that a leader has "asked" them to support: if the measure has enough support in the party, the leader will proceed - a very explicit model of so-called "political capital".
Though there are many concerns about liquidating any given transaction, even in a conventional market, there are ideologies which hold that the risks are outweighed by the efficient rendezvous. In greenhouse gas emissions trading this is particularly non-controversial as the whole atmosphere of Earth can reasonably be seen as one uniform body affected almost equally by emissions anywhere on Earth. There are thus almost no local effects, and only a measurable and widely agreed climate change effect, of a greenhouse gas emission, justifying a "cap and trade" approach. Somewhat more controversially the approach was applied even earlier to sulfur dioxide emissions in the United States, and was quite successful in reducing overall smog output there.
In most applications of such methods, however, the comprehensive outcome of the transaction is not so easily measured or universally agreed. Some theorists assert that, with appropriate controls, a market mechanism can replace a hierarchy, even a command hierarchy, by ordering actions for which the highest bid is received:
An infamous example is the assassination market proposed by Timothy C. May, which were effectively bets on someone's death. This has since been generalized into the prediction market idea which the Pentagon proposed to operate as part of Total Information Awareness—however this proved controversial as it would theoretically let assassins predict and then benefit from their predictions, which they would cause to come true. This is however a problem even with the commodity markets and any other financial markets where a single person's choices or fate might be influenced, predicted, or decided by someone already in the market.
Less controversial applications of bid and ask matching include: