Managerial Application 144

Game Theory at the FCC

One of the most successful game theory applications has been in the design of FCC auctions used to allocate electromagnetic spectrum, a highly valuable and finite public resource. In the design of the auction process, the FCC has relied on advice from top game theorists at Stanford, Yale, and other leading universities. The agency has generally adopted a standard English auction in which the winner pays what it bids, and everyone can see all bids as they are made. Game theory research shows that open auctions stimulate bidding, whereas sealed auctions foster restraint for fear of needlessly paying too much.

Although the FCC initially favored auctioning off vital spectrum licenses all at once to make it easier for bidders to assemble efficient blocs of adjoining areas, this approach entails a nightmare of complexity. Complicating the problem is the fact that bidders must be allowed some flexibility to withdraw bids when adjoining areas are sold to others. If all offers could be withdrawn easily, however, the integrity of the process would suffer. A sequential auction, where areas are put up for bid one at a time, also involves problems because it denies participants the opportunity to bid more for economically efficient blocks of service areas. Winning bidders in a sequential auction have the potential for a snowballing effect where one success leads to another, and another, and another. After considering a wide variety of options, the FCC adopted a modified sequential bidding approach.

How does it work? Consider the PCS spectrum auction, which began on December 12, 2000, and ended on January 26, 2001. After 101 rounds of bidding, 422 licenses covering 195 markets, including New York, Los Angeles, Chicago, Boston and Washington, DC, were allocated. The FCC's competitive bidding process allowed for rapid deployment and ensured that spectrum went to the highest value use. The American taxpayer also benefited when the PCS auction raised $16,857,046,150!

See: Jacquie Jordan, "Triton PCS to Acquire Excess PCS Spectrum from Ntelos," The Wall Street Journal Online, December 12, 2001 (http://online.wsj.com).

sensitivity analysis

Limited form of computer simulation that focuses on important decision variables

Instead of using complete probability distributions for each variable included in the problem, results are simulated based on best-guess estimates for each variable. Changes in the values of each variable are then considered to see the effects of such changes on project returns. Typically, returns are highly sensitive to some variables, less so to others. Attention is then focused on the variables to which profitability is most sensitive. This technique, known as sensitivity analysis, is less expensive and less time-consuming than full-scale computer simulation, but it still provides valuable insight for decision-making purposes.

Computer Simulation Example

To illustrate the computer simulation technique, consider the evaluation of a new minimill investment project by Remington Steel, Inc. The exact cost of the plant is not known, but it is expected to be about $150 million. If no difficulties arise in construction, this cost can be as low as $125 million. An unfortunate series of events such as strikes, greater than projected increases in material costs, and/or technical problems could drive the required investment outlay as high as $225 million. Revenues from the new facility depend on the growth of regional income and construction, competition, developments in the field of metallurgy, steel import quotas and tariffs, and so on. Operating costs depend on production efficiency, the cost of raw materials, and the trend in wage rates. Because sales revenues and operating costs are uncertain, annual profits are unpredictable.

Assuming that probability distributions can be developed for each major cost and revenue category, a computer program can be constructed to simulate the pattern of future events. Computer simulation randomly selects revenue and cost levels from each relevant distribution and uses this information to estimate future profits, net present values, or the rate of return on investment. This process is repeated a large number of times to identify the central tendency of projected returns and their expected values. When the computer simulation is completed, the frequency pattern and range of future returns can be plotted and analyzed. Although the expected value of future profits is of obvious interest, the range of possible outcomes is similarly important as a useful indicator of risk.

The computer simulation technique is illustrated in Figures 14.6 and 14.7. Figure 14.6 is a flow chart that shows the information flow pattern for the simulation procedure just described. Figure 14.7 illustrates the frequency distribution of rates of return generated by such a simu-

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