- Entering wine competitions costs $x, and winning gets you $y (>x) in increased profits
- Wine competitions A, B and C are in that order chronologically, and all give medals to a third of entrants
- There are nine wines, called 1-9
- There is fair agreement between wine authorities at the competitions on good wine, such that if your wine wins one competition it is almost certain to win the next.
What should the wine sellers do to maximize money? All enter A. Three win. Those three go on to enter B, and its winner enters C, while the others stay out unless y is radically > x, as they are likely to lose again.
That means that A makes $9x, B $3x and C $x. An easy way for B and C to increase their profits is to be less predictable then. At the extreme of unpredictability, all wines would enter all competitions, and A, B and C would all make $9x profits, and medals wouldn’t mean much about wine quality.
Of course when people notice that prizes correlate less with wine quality they ignore prizes more, and competitions must charge less entry. In reality most consumers get virtually no evidence of the quality of wine by drinking it, so they are only likely to notice whether better wines get prizes if someone pays attention to the statistics and finds no correlation between winners in different competitions. Someone did this, and found that, prompting me to try to explain it. What do you think?