# Tournament Theory

Economic theory traditionally explains income differences in terms of marginal productivity. If we have a mason who can lay 50 bricks per hour, we expect him to earn twice as much as the mason who can lay only 25 bricks per hour because there would be a profit opportunity for building contractors if any other wage rate existed. If the more productive mason works for less than twice as much as the other, everyone would want to hire him and no one would hire the less-productive one. Only when his wage is exactly twice as high, exactly paralleling the difference in productivity, would people be equally willing to hire either.

This way of explaining wage differentials suggests that the very large differences in income are the result of equally large differences in performance. However, there is an alternative explanation that says that in many cases relative differences in performance, not absolute differences, determine earnings. This explanation of wage differences in terms of relative performance is often called tournament theory. One place where this explanation should work is in contests with winners and losers. For example, consider two almost equally able gladiators fighting in the arena of ancient Rome. Small differences in ability (or luck) could result in a huge difference in reward--one could die and the other live.

Though gladiators are no longer part of our world, there are still cases in which winners matters a lot, and as a result, small differences in ability (or luck) can cause large differences in reward. The sports world has many examples. The winner of Olympic gold may triumph by a tiny fraction of a second, but that tiny fraction often is translated into huge amounts of money via product endorsements. The practice of law also has winner-take-all situations. The level of a lawyer's skill may be less important than how he ranks relative to other lawyers with whom he competes.

We have limited amounts of time to read, enjoy music, or attend movies. Given our limited time, we are selective and willing to pay a substantial premium for a product that is better. Of the many talented pianists, only the top few earn enough to live by concert performances alone, but they earn substantial sums. Two writers may be nearly equal in talent, but when people have a limited amount of time to read, the vast majority may end up reading the work of the one that is only slightly better. Though at first glance these situations seem very different from those involving athletics, the way that pay is determined may be very similar.

Another place where relative ability may matter a great deal is in the managerial ranks of corporations. There are only limited numbers of promotions available, and they are usually determined by relative performance. Only one person can be CEO of a company at a time, and small differences in ability among those contending for the top spot can result in large differences in rewards. Further, it may be in the interests of the company to structure pay so that the winner makes very large sums as a way of spurring on those lower in the hierarchy. The primary reason for the high pay given to the CEO may be to give those lower in the hierarchy an incentive to work hard, not to give the CEO himself the incentive to perform well.