English Auction

The English auction takes different forms. To keep our understanding simple we will look at what could be called a continuous ascending price auction.

In this auction each bidder sits with a button and a giant clock indicates a starting price. Each bidder has to press her button to indicate that she is willing to receive the object at the displayed price. If two or more bidders have their buttons pressed the price continuously moves up. The thing about the buttons is that if a bidder takes her finger off the button, it becomes deactivated for the rest of the auction. So a bidder cannot decide that she does not want the object, takes her finger off the button, and then decide that she actually wants it.

When a bidder takes her finger off her button we say that she has dropped out of bidding. Typically, as the price indicated by the clock increases continuously bidders may drop out one by one till only two bidders remain. Then the moment one of them drops out the price on the clock stops and the remaining bidder wins the object at that price.

It is possible that both remaining bidders drop out at the same price, it is even possible that there are three or more bidders remaining and all of them drop out at the same time. That situation is called a tie. The price stops when all remaining bidders drop out at the same time, and one of them is awarded the object (either randomly or based on who had registered for the auction first) for the price at which the clock stopped.

Bidding Strategies

It is a dominant strategy to bid your true value in an English auction. The reason is very simple. Imagine yourself in front of the button that you press to indicate if you are willing to purchase a fine bottle of single malt for your husband (just saying). Your value for this gift that your husband will appreciate is $300. It is $300 because you do not think it is worth spending more than that for this bottle (or for your husband).

The price starts at $0. Are you pressing the button. Of course, yes! The price has reached $200. Are you still pressing the button? I hope so, because you are willing to pay up to $300 for the bottle and it is still less than that. Regardless of whether the other bidders are bidding or not, you should not find any reason to release your button till the price reaches $300. After all, if all your rival bidders drop out of bidding before the price reaches $300, the price rise will stop, and you will win the bottle.

You should not want to keep the button pressed beyond $300. Because, then if others drop out and you win, you will be paying a price that is more than your value. This is the simple reason why we predict that in an English auction bidder will bid (up to) their true values for the object as part of the dominant strategy equilibrium.