Competition The Birth of a New Science

Preface Competition is a surprisingly difficult concept even to define. Modern lexicographers have failed repeatedly to improve on the definition given by Samuel Johnson in his 1755 work Dictionary of the English Language. In it he declares "competition" to be a noun meaning "the act of endeavoring to gain what another endeavors to gain at the same time; rivalry; contest." Yet even this definition is unacceptably narrow, since it limits to two the number of admissible competitors. Auctions, spelling bees, primary elections, horse races, and track and field events, as well as golf, tennis, and bowling tournaments, typically allow large numbers of hopefuls to compete. At the very least, Dr. Johnson's definition should be amended to read "what others endeavor to gain." Like solitaire, crosswords, picture-, and other sorts of puzzles may be viewed as single-player games. All such games can, in principle, be solved mathematically. Although it might take the fastest conceivable computer millions of years to crack a particularly difficult puzzle, it is at least possible to define what is meant by a solution, and to specify the steps a computer would have to perform in order to find one. The same cannot be said of contests open to three or more competitors, since there is no universally accepted definition of a solution. As a result, leading authorities can disagree as to which, if any, of several proposed solutions for a particular many-player game is valid. Two-player games can go either way. Those of the "zero-sum" variety, in which the winner wins only what the loser loses, are almost as solvable as puzzles and solitaire. Those that are not zero-sum are nearly as insoluble as many-player games. It is indeed unfortunate that the forms of competition that most directly affect human welfaresuch as wars and commercial competitionare rarely zero-sum, and typically involve more than two competing factions. It is worth noting that, whenever many-player games such as Scrabble and Monopoly are contested at the tournament level, the rules are altered to transform them into two-player zero-sum games. Many-player and non-zero-sum games are simply too confusing for tournament play. With three or more players, there would be no end of complaints from alleged victims of collusion. It was not until 1944 that John von Neumann and Oskar Morgenstern developed a truly workable definition of competition. It took them an entire chapter of their groundbreaking Theory of Games and Economic Behavior to explain what they had done. From the realization that a game isfor analytical purposesnothing more than a book of rules, they distilled a concise (if forbiddingly technical) definition of a game. Only gradually did it become clear that all forms of competition can be made, with but little modification, to fit their definition. Indeed, more than sixty years after they wrote, no one has identified a form of competition that seems incompatible with the von NeumannMorgenstern definition of a game. In 1950, Harold Kuhn developed the simpler and more graphic, yet logically equivalent, form of that definition to be found in Chapter 3. Though dictionaries may never include the entry "com'pe ti'tion (kom'pe tish9'un), n. See game," the emerging science of competition has yet to discover anything suggesting that such an entry would be misleading. You won't find many departments of competition science listed alongside those of physics, chemistry, and food science in the catalogs of leading colleges and universities. There is as yet no Journal of Competition ScienceCase, James is the author of 'Competition The Birth of a New Science', published 2007 under ISBN 9780809035779 and ISBN 0809035774.