doping

Michael Phelps is a Dolphin. That was the headline of Drudge. Bunch of articles up about his smashing the record on the 4x100. I really, really, really, really hope we don't learn in a few weeks that he's been doping.

I wrote up a single prisoner's dilemma model of doping back in grad school that suggested to me it was individually optimal to dope, even though it collectively reduced social welfare since the costs spent on doping were too high. The basic idea in the model was that the action to dope both increased the chances of that person winning (and thus the payout), and also decreased the expected payout to someone else. In other words, you got better, but because sports are zero sum, winner take all games, your opponent did worse. It was a dominant strategy to dope because if the other person didn't dope, then you should dope (since it increased your expected payout) and if the other person did dope, then you should definitely dope since in that world you needed to dope to improve your chances of winning (which were now worse since your opponent was doping). From there it was simple to show that it was a nash equilibrium that all players doped.

What I thought was interesting, though, was that not only did all people incur a cost to dope, but because the gains to a player negated the gains to the other player, in equilibrium the doping advantage to one person was washed away by the doping advantage given to the other person. It was a simple model, so basically I just made doping increase your payout by A, and decrease your opponent's payout by B. Then when everyone doped, you got an increase in your payout equal to A-B. In other words, you had some ambiguous effect on individual performance because everyone was doping, and thus negative externalities were (-B) were imposed on all other players in the match.

There was enough in that simple model to make me want to look at it more, but I never did. But I still think it's probably right that you've got basically an arms race when it comes to doping. It's inefficient to dope, collectively, because the outcome is basically the same if everyone is doping (e.g., the batter is a bigger hitter, but the pitcher pitches much faster and more accurately, plus the fielders are faster), but now society is incurring the costs associated with doping, whatever those are (mainly the expenditures and the health costs).

Not really sure how to deter it, particularly when the probability of detection seems to be falling given the never-ending breakthroughs in sports medicine. At some point, I suspect the costs to enforce anti-doping rules are going to exceed the costs to society of having athletes dope. When that point comes, we may have to accept the fact that a certain amount of positive doping is efficient, and to try and get it down anymore is going to be worse.