Game Theory and Decision Support Systems

Game Theory and Decision Support Systems

The connection between game theory and Decision Support Systems is exemplified by the 1994 auction of radio spectrum bandwidth by the Federal Communications Commission (FCC) to firms interested in its use for personal communications services (PCS): pocket telephones, portable fax machines and wireless computer networks. The 2500 formerly military spectrum licenses were estimated to be worth $10.6 billion, even though telecommunications experts [i]“scoffed” at that price, and the auction was planned at a time when speculation in the future of US telecoms was very high.

History of Frequency Allocations

In the early days of spectrum licensing, the FCC had a system that simply gave away the rights to interested parties. The system revolved around administrative decisions to assign bandwidth. Interested parties filed applications for licenses and hearings were held to determine which applicant the most worthy. This method proved inefficient, with many licenses going unassigned. In 1982, Congress stepped in with the decision to go to a lottery system assigning the licenses randomly among any who applied. This greatly improved the speed of the system, but the chance of a windfall attracted many applicants speculating on easy riches. For one lottery of cellular telephone frequencies there were over 400,000 applications. In a 1989 case, a group of dentists going by the name RACDG Partnership was chosen by lottery to operate the cellular telephone system on Cape Cod. The dentists quickly turned around and sold their license to Southwestern Bell for $41 million. By Commerce Department estimates, the value of cellular licenses the FCC gave away during the 1980’s alone was over $46 billion[ii]. Trying to capitalize on the value of future technologies, Congress in 1993 passed legislation authorizing the FCC to create an auction system to replace the lotteries.

The idea of an auction for bandwidth was not a new one. Earlier in 1993, the Australian government had authorized an auction for the airwaves used for satellite TV service. This attempt however met with a most unpleasant conclusion. When bidding was complete, the government was pleased that their wildest estimates had been achieved when an investment group by the name of Ucom Proprietary LTD. submitted a bid of $152 million. Problems arose however when the intent of Ucom not to pay that price soon became apparent. Ucom deliberately defaulted on the bid, forcing the government to consider the next highest bid, also from Ucom, who by this time had learned of their competition’s highest bid, and continued to default until the government reached one of their bids just slightly higher than the competitions. The final amount Ucom paid was $84 million, far below the original winning bid.

As disappointing as the Australian’s attempts were, they pale when compared to a 1990 frequency auction in New Zealand. Innovators in the auctioning of airwaves, the government selected a second-price auction format. With this form of auction, the highest bidder wins, but pays whatever the second place bid amount is. The rational was that bids would reflect the amount the bidders truly valued the licenses for. The results however were nothing short of a disaster. In one case, a firm that bid NZ$7 million paid the second-place price of NZ$5,000. Another bid won at NZ$100,000 went for the second bid price of NZ$6. The public outrage was magnified simply by the ease with which it was to confirm the value of the bandwidths to the firms in their winning bids, and then seeing the bargain basement price actually paid. The major flaw in the New Zealand approach was that a reserved, minimum bid was not put in place. The final total for cellular licenses was NZ$36 million, far below the NZ$240 million originally forecast.

Which Auction to Choose?

There are four main types of auctions from which a seller can choose: the English auction, Dutch auction, sealed first price, and sealed second bid. An English auction is the familiar “going, going …gone” type of auction won win the second place bidder simply gives up. With a Dutch auction, the price starts out high and ends when it’s dropped to a point that someone is willing to pay. The sealed first price involves bidders submitting sealed bids with the winner being the highest bid. The earlier example from New Zealand demonstrates how the sealed second bid works: the winning high bidder pays the amount of the second highest bid.

The history of the second bid type of auction can be traced back to the economist William Vickrey of Columbia University, who in 1961 published a paper that analyzed game theory and its application to auctions. Vickrey, who won the Noble Memorial Prize in Economics in 1996, studied what economists call “private value” auctions, in which each bidder’s value for the item is independent of the values of the other bidders. The reasoning was that if you are bidding on an auction item simply because you “like it”, the value it has to other bidders is irrelevant to you. After looking at the first three auction types, Vickrey developed the sealed second bid. Although the second price seems the most unnatural approach to bidding, it is the one with the simplest optimal bidding strategy: Just bid the amount equal to the value of the item for you.

Suppose, for instance, a bidder is willing to pay up to $100 for an old Coke bottle. What will happen if he bids less than $100, say $90? If the highest rival bid is $80, he’ll win and pay $80; but the same thing would have happened if he had bid $100. If the highest rival bid is $120, he'll lose; and again the same thing would have happened if he had bid $100. But if the highest rival bid is $95, he’ll lose the auction, whereas if he had bid $100 he would have won the bottle for $95. So bidding $90 never improves his situation, and sometimes makes him lose an auction he would have liked to win. In a similar way bidding more than $100 never improves his situation, and sometimes makes him win an auction he would have liked to lose. In a second-price auction, the strategy of honesty is the best policy[iii].

The Winner’s Curse

Imagine that a jar of pennies is being sold in a sealed first-price auction, with five bidders participating. The jar holds $10 in pennies, but none of the bidders knows that; they must estimate the value of the pennies by the size of the jar. The bidders independently estimate how much the jar is worth. One bidder guesses the right amount, $10. Two other bidders estimate the jar holds $8 and $12, respectively. The final pair of bidders estimates the value at $6 and $14, respectively. Since all of the bidders placed a bid consistent with what they think the jar is worth, the winning bidder will pay $14 for $10 in pennies—what economists call the “winner’s curse.” Even if the jar is sold in a second-price auction, the bidder will overpay by two dollars. Although on average the bidders are correct about how much money is in the jar, the winner is far from correct; that bidder is the one who has overestimated the value the most. In an1983 experiment at Boston University, economists Max Bazerman and William Samuelson had M.B.A. students bid on a jar full of nickels in a first-price auction; on average the winning bid was 25 percent more than the jar was actually worth[iv].

To protect themselves from the winner’s curse bidders must change their rational. With any auction, there is a chance some bidders will overestimate the value of an item. If everyone bids what they think the item is worth, the person with the highest overestimate will win and pay too much for the item. This leads to the safe strategy of assuming one has overestimated the value of an item, requiring a bid somewhat less than they value the item. If the bidder really has overestimated, this strategy will bring their bid more in line with the actual value of the item. If the value of the item was not overestimated, lowering the bid may hurt one’s chances of winning the auction; but it’s worth taking this risk to avoid the winner’s curse. This reasoning applies not just to bidders for jars of pennies but also to airlines bidding for landing rights, football teams bidding for free agent players, and bidders in any situation where the item has some intrinsic value about which the bidders are uncertain— what economists call “common value”[v] settings.

The FCC Bid

The task at hand for the FCC was to design an auction system that would avoid the difficulties experienced by other governments. They faced many questions: Should they use an open or closed bidding system? Could they choose rules that would ensure the licenses went to firms that would use them quickly? Could they prevent loopholes that would allow companies to unfairly exploit the system?

There were other problems facing the FCC as well. For instance, what if a company bidding on a license in one area would like to aggregate it with another area? Because of economies of scale, a company bidding on a license for Southern California may place a higher value on it if they thought they could also secure the license for Northern California. Separately, the bid for each may have far less value to two separate entities. To address this problem, the FCC decided to auction all licenses simultaneously in multiple rounds, enabling firms to aggregate in markets they so desired, and withdraw from others that were priced out of their range. All that was left was to decide upon the auction type that would insure the best return for the government while encouraging a fast entry into the market for the desired PCS devices.

The Outcome

Game theory researchers suggested to the FCC that an open English auction would raise the most revenue, since it would allow bidders to gather the most information and allow them to bid more confidently. The FCC decided to follow that advice, with a slight variation: In each round of the auction the bidders placed bids secretly in enclosed booths; the FCC then announced the new high price without saying who had bid it. By hiding the bidders’ identities in this way, their ability to engage in retaliatory bidding against each other or in collusion to keep prices down was greatly lessened.

By all measures, the auction was a spectacular success. By 2001, the spectrum auction had brought in over $42 billion, with more licenses to be sold, far exceeding the $10 billion estimates early on. However, the more profound success may lie in the fact that the licenses were now in the hands of organizations that were truly committed to getting products to the market in a timely manner. Within two years of the first spectrum auctions, wireless phones based on the new technology were on the market.

How it Relates to Decision Support Systems

The basic definition of a DSS by Marakas is:

A decision support system is a system under the control of one or more decision makers that assists in the activity of decision making by providing an organized set of tools to impart structure to portions of the decision-making situation and to improve the ultimate effectiveness of the decision out come.[vi]

In today’s worldwide marketplace, there is much being offered through auctions to the highest bidder. Whether its drilling rights for an oil company, logging rights for lumber, or excess telecom equipment on eBay, there are many instances in which the proper strategy for an auction, whether one is the buyer or seller, is ultimately the key to long term success. By using game theory as a tool in designing your decision support, a bidder or seller can be better assured that the final results of an auction will truly reflect the value of the item, service or commodity purchased.

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