At a recent U.S. Open, one of the four major golf tournaments, the pro finishing first won $625,000 while the second-place player won

$370,000. The winnings continue to fall quickly, so that the pro coming in tenth won only $78,863. What is the advantage to the Professional Golf Association (PGA), which runs the tournaments, of having such a steep pay scale? Why not, instead, let the top five finishers share the same prize? How does the steepness of the pay scale affect the willingness of golfers to collude?