## Game Theory and Auction Strategy

Game theory dates from the 1940s, when mathematician John von Neuman and economist Oskar Morgenstern decided to turn their card-playing ability into a more general theory of decision making under uncertainty. They discovered that deciding when to bluff, fold, stand pat, or raise is not only relevant when playing cards, but also when opposed by aggressive competitors in the marketplace. Rules they developed are increasingly regarded as relevant for analyzing competitive behavior in a wide variety of settings. One of the most interesting uses of game theory is to analyze bidder strategy in auctions.

The most familiar type of auction is an English auction, where an auctioneer keeps raising the price until a single highest bidder remains. The advantage of an English auction is that it is widely regarded as a fair and open process. It is an effective approach for obtaining high winning bid prices. Because participants can see and hear what rivals are doing, bidders often act aggressively. In fact, winners sometimes overpay for their winning bids. The so-called winner's curse

Where overly aggressive bidders pay more than the economic value of auctioned-off items sealed-bid auction

Auction where all bids are secret and the highest bid wins

Vickrey auction

Where the highest sealed bid wins, but the winner pays the price of the second-highest bid

### Dutch auction

Winning bidder is the first participant willing to pay the auctioneer's price winner's curse results when overly aggressive bidders pay more than the economic value of auctioned-off items. For example, participants in the bidding process for off-shore oil properties in the Gulf of Mexico routinely seemed to overestimate the amount of oil to be found.

Another commonly employed auction method is a sealed-bid auction, where all bids are secret and the highest bid wins. Local and state governments, for example, employ the sealed-bid approach to build roads, buy fuel for schools and government offices, and to procure equipment and general supplies. A compelling advantage of the sealed-bid approach is that it is relatively free from the threat of collusion because, at least ostensibly, no one knows what anyone else is doing. The downside to the approach is that it could yield less to the government when airwave space is auctioned off because the approach often encourages bidders to act cautiously.

A relatively rare sealed-bid auction method is a Vickrey auction, where the highest sealed bid wins, but the winner pays the price of the second-highest bid. The reason for this design is that the technique tends to produce high bids because participants know beforehand that they will not be forced to pay the full amount of their winning bid. A disadvantage of the technique is that it creates the perception that the buyer is taking advantage of the seller by paying only the second highest price.

Another uncommon auctioning method is the so-called reverse or Dutch auction. In a Dutch auction, the auctioneer keeps lowering a very high price until a winning bidder emerges. The winning bidder is the first participant willing to pay the auctioneer's price. A disadvantage of this approach is that bidders tend to act cautiously out of fear of overpaying for auctioned items. In terms of the FCC's sale of airwave space, a Dutch auction might yield less to the government than an English auction. Offsetting this disadvantage is the fact that winning bidders would then be left with greater resources to quickly build a viable service network.

In auctions of airwave space for new communications services, the FCC uses a number of auction strategies to achieve a variety of sometimes conflicting goals. To raise the most money while creating efficient service areas and encouraging competitive bidding, the FCC uses all four basic auction strategies. To better understand the motives behind these auction strategies, it is necessary to examine game theory rules for decision making under uncertainty.

maximin criterion

Decision choice method that provides the best of the worst possible outcomes