Krishna’s Auction Game Theory Explained

Krishna’s Auction Game Theory Explained

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An auction is a transaction which places people in competition with one another over the purchase of a specific item. Bidders will create a personal valuation on the item in question, which is unknown to other bidders or the seller. A seller may also have a specific value that they want to receive from the item. Although there are different rules in place for different auction, the outcome is generally universal.

Auctions are used to sell or buy any item. Auctions also tend to be anonymous. Under Krishna’s auction game theory, the seller and bidders are also representatives of a mathematical game which requires strategic actions by each player involved so that someone must win and someone else must lose.

Who Are the Players in the Auction Game Theory?

In most circumstances, the players in the auction game theory are the buyers and the sellers. The first actions that are taken in the auction will be the installation of a reservation price and a set of bid functions. Each bid function can them map the value of the player or the cost to the seller within the context of a bid prices. Then, evaluating the balance of profit and loss between the strategic actions of all parties playing the game, a final winner can be declared.

There are two game theory models that can apply to this type of transaction.

1. Private Value Model.
In this auction game theory model, each bidder assumes that every other competing bidder has given an item a private value to the item in question that is random. The bidder who intends to win must then determine the range of values that other bidders have and be willing to exceed it. Each bidder assigns an individualized value to the item.

2. Common Value Model.
In this auction game theory model, the bidder assigns a value to the item being purchased that is based on an accurate valuation. Every other bidder is assigning the same value in their estimates as well. Instead of having independent value, there is a common value assigned.

There is a third model, sometimes called the Affiliated Values Model, which combines components of private and common value. The strategy of the bidder in this additional model would depend on private signals and common values to determine a comfortable final purchase price.

The Winner’s Curse in Auction Game Theory

When the common value model is used during an auction, each bidder is basing their game play on their own personal estimates of the common value of the item. This means the winner of the auction is going to be the individual who had the highest overall value estimate for the item in question.

The results of the auction show that those who were also bidding on the same item had a lower value estimate. This means the winner is left with the impression that they paid more than necessary to obtain the item in question.

Yet the winner’s curse doesn’t apply elsewhere because bidding strategies and individualized values take precedence over a common estimated value. This is why someone can feel like they got a great deal when they purchase a rare automobile for $5 million, yet the bidder next to them feels like they were smart by stopping their bidding at $1 million.

Classifications and Auction Game Theory

There will always be independent variables to any game that is being played, especially within the context of an auction. Some bidders are going to be very averse to risk, only bidding an amount that they feel will give them the highest probability of obtaining what they want. This allows them to place what they feel is a reasonable bid that limits their risk.

Sellers can also change the terms of the game by changing how the auction transaction takes place. Instead of one final selling point, a seller could incorporate royalties, incentive payments, or production costs into the price function to pad their bottom line. This would change the common value perspective, forcing bidders to potentially pay more for at item even though it has a lower perceived value.

Some classifications separate bidders into two different groups based on their personal context. A dealer, for example, might pay less for an antique item than a collector would pay, so the seller would want to promote their item to the demographic that they feel will pay the most for what they have.

Krishna’s auction game theory looks at economics in this frame. Every purchase we make is essentially an auction where we’ve assigned a specific value to the item.