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Game theory in the popular press.

The Five Percent Solution

Mathematical Association of America
Keith Devlin
May 1, 1996
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As mathematicians, we are rarely satisfied with less than the complete solution. In fact, even that is not enough. Once a problem has been solved, we look for shorter, cleaner, more elegant solutions. That is the nature of mathematics. For the engineer, searching for the "perfect" solution is a luxury that can rarely be afforded. There are deadlines to meet, and delay increases the cost. Find a solution that works within a certain toleration--that's the name of the engineer's game.

For the business manager, things are far less clear-cut than in either mathematics or engineering. The world of people, business processes, economics, finance, and marketing is orders of magnitude more complex ("messy" might be more appropriate) than the world of mathematics. For the business manager, a "five percent solution" is often worth a considerable search. A small increase in efficiency can mean cost savings of millions of dollars. A five percent edge over the competition can mean the difference between domination of the market and commercial extinction.

There is, then, a wide gulf that separates the worlds of mathematics and business. At least in terms of what constitutes a "solution" to a problem. But that gulf does not prevent the world of business being able to profit from the odd bit of mathematics from time to time.

Mathematical disciplines such as statistics, optimization theory, probability theory, queuing theory, control theory, game theory, and operations research are all used routinely in making difficult choices in public policy, health, business, manufacturing, finance, law, and various other human endeavors. Mathematics can play a significant role in arriving at decisions in all walks of life-making policy decisions connected with global warming, deciding on the most economic way to generate electric power, making a profit in financial markets, approving new drugs, weighing legal evidence, flying aircraft safely, managing complex construction projects, choosing new business strategies, and so forth. But the role played by mathematics in such domains is rarely that of "providing the solution." Far more commonly, the mathematics can "influence" or "inform" the decision making process.

Take game theory as an example. In its modern form, it is the brainchild of the mathematician John von Neumann. Game theory models the results of actions of competing parties in competition, with each acting in its own self-interest. In 1994, the Nobel Prize in economics was shared by John Harsanyi and the mathematicians John Nash and Reinhard Selten for their introduction of several different concepts of market equilibria, situations in which each party is in an optimum position relative to its competitors. It's fascinating mathematics. And it can, occasionally, be "applied" in real-world situations. But for the most part, when it comes to making many real, human decisions, game theory can provide at most a "possible scenario" or an "alternative view", and occasionally, maybe, it can suggest other solutions. For despite all the impressive mathematics of game theory, the model for most real-life conflicts is the age-old game of 'chicken'. (Remember the James Dean movie where the two cars race for the cliff edge?) In that kind of game, human experience, courage (foolhardiness?), and instinct rule the roost. The psychologist is probably better equipped to come up with the best solution than the mathematician.

I was prompted to reflect on the role of mathematics in the business world by a conversation I had recently with a business manager. He was commenting on the use of the word "Quality" in the business world. "Before the introduction into business of tools like the Gaussian distribution, the fishbone diagram, the Pareto chart, and so on," he observed, "the word 'quality' was soft." Everyone felt they could recognize "quality" when they saw it, but no one could define or measure it. But a few fairly simple mathematical ideas made all the difference.

I was sufficiently intrigued by all of this to check out and read a recent book on quality control and improvement in business, "Accelerating Innovation," by Marvin Patterson, Director of Corporate Engineering for Hewlett-Packard. The book is littered with graphs and charts and other mathematical ideas (including some stuff from decision theory). None of it would earn you a college credit from a mathematics department. But--and I have to take this on faith since I have no knowledge of the world of business management--this assortment of simple mathematical ideas can be worth millions of dollars to a company in the competitive marketplace.

At the very least, what I discovered suggests that a good education in mathematics could be a tremendous asset to the upwardly mobile young business executives. Providing, of course, that they can rid themselves of the overpowering urge to go for the 100 percent solution.

It also, dare I suggest, casts a more positive light on the business majors in our college and university mathematics classes who keep asking the eternal question, "What's the use of all this?" From their perspective, it's exactly the right question to ask. And the answer we should give is, "You go and discover that . . . and make a million bucks as a result."