More game theoretic analysis of Landis and Lance.

Last Friday, I blogged about an editorial in the LA Times by Michael Shermer where he used game theory to explain why he believes Floyd Landis’ story is believable. Basically, Shermer says that pro cycling would be in a Nash equilibrium that would lead cyclists to be silent about the doping as long as they each had something significant to lose by coming forward. However, once Landis lost his wife, home, and cycling career and, therefore, no longer had anything to lose, Shermer argues that it is expected that he would spill the beans on the “cycling mafia”, as Tyler Hamilton has called it.

Another Game Theoretic Analysis

This week, I received an interesting analysis by my friend and fellow cyclist, Professor Jim Kearl, who teaches economics at Brigham Young University. Jim provided a game theoretic argument suggesting that some of Landis’s story is hard to believe. The crux of his argument, as I see it, is that Landis is claiming that there were people who had knowledge of the doping operation who would not have anything to lose if they came forward. As such, the doping mafia or “cartel of silence” as Professor Kearl says, would not be in equilibrium. Here is Jim's analysis:

There is a good "game theory" argument for why Landis cannot be believed and Armstrong, at least on the doping issue, can.  To wit: Cartels are unstable.  Landis's argument is that Armstrong's doping was "public" in the sense that it involved team members, bus drivers, and team managers.  To keep this quiet for 10+ years, implies a stable "cartel of silence" among a fairly large, and changing, group of people. It simply isn't credible to believe that such a cartel could exist or persist.  This is particularly the case when Armstrong's team changed over the 7 years he was winning, and some of the riders were, more or less, "fired" and replaced by others and would likely have been unhappy and even less beholden to the "cartel of silence." This doesn't mean there wasn't doping; it just means that any doping would have been "private" (that is, "individual") and, it follows, not known to Landis.  Put differently, the only doping he would know about is his own.  Everything else has to be conjecture on his part unless one is willing to believe that a "secret" can be kept by a fairly large, and changing, group of people for years.

I definitely find Jim’s analysis interesting and, in my mind, it suggests two main possibilities. One possibility is that Landis is lying on at least some details in his stories. This is not hard to believe given his track record. Another possibility is that the “cartel of silence” involved only people who had enough incentive to keep them from revealing the doping “secret.” In other words, going back to Shermer’s analysis, if the only people who knew about Lance’s doping would lose something of significance by breaking the code of silence, then, I think, a game theorist like Shermer would argue that a Nash equilibrium of silence may exist--even for several years. Here are my thoughts on this possibility. 

Other Widespread Doping in Sports

First, there are other times when widespread doping has occurred for several years in pro sports without our knowledge--for example, Operation Puerto and Festina in cycling and Balco in baseball and track. Jim's analysis suggests that those involved in these doping operations either were unaware of other athletes who were doping or they kept the secret. Additionally, from what I know about the Balco case, Victor Conte is said to have networked among professional athletes to get them to refer others to him. In that case, athletes would be aware of others who were doping suggesting that a “cartel of silence” was stable for several years. 

Cyclists' Incentives

What about the incentives of the cyclists? Were they high enough to maintain the silence even after being fired? I personally believe that the incentives were high enough that if cyclists who were doping knew others on their team were doping that they would rarely, if ever, come forward. From Tyler Hamilton’s and others’ comments that a cycling mafia exists and from documented events where Lance chased down members of the peloton who were threatening to break up the cartel, I think there is evidence that individuals in the peloton would keep their involvement in doping secret, even after moving from one team to another. They each had a lot to lose including sponsorships and retracted awards if they admit to doping in the past. Even so, some of Lance's former teammates have come forward to break the cartel. A few of Lance's former teammates (other than Landis) who have come forward are documented at this link. 

Non-Cyclists' Incentives

So what about those non-racers that Landis alleges were involved, including bus drivers and managers? What about their incentives? In my view, managers fall into the same category as the riders. They have much to lose in both fame and fortune by exposing the doping that they were aiding.

As for bus drivers, they are the best evidence to me that Landis’s story may have some holes in it. It’s possible the bus driver was also a manager or someone who had significant incentives to keep silent but, if not, it makes you wonder why they kept silent. Were they paid off? Interestingly, we do have evidence that others with little or no skin in the game did not keep silent. For example Lance’s masseuse, Lance’s former teammate Frankie Andreu and his wife Betsy, Lance’s former teammate Steve Swart and others as discussed at this link.

Other Longstanding Cartels of Silence

As for other evidence that a cartel of silence could be maintained--especially in the presence of significant incentives--I am aware of several massive financial statement fraud cases that went on for years, even decades, and a cartel of silence was maintained. For example, Bernie Madoff's famous $50 billion Ponzi scheme went on for at least two decades with numerous individuals helping maintain the operations. Bernie's scheme was so involved that he needed the assistance of numerous individuals just to create fictitious documents and records. Even so, nobody came forth to break the cartel of silence.

Conclusions

So what does all this game theoretic analysis mean? First, in my view it doesn’t prove anything either way. Rather, it suggests that some parts of Landis’s story are more plausible than others. In doing so, it provides some leads that the fraud investigators will want to follow. If I was conducting the investigation, I would want to know who the bus driver was and why he never said anything to anyone about the alleged transfusions that Landis tells about. Second, it suggests that, if Landis is to be believed, then to the extent that cyclists and managers knew of others who were doping, they kept the “cartel of silence” for quite a while. We could expect strong incentives in place to ensure this behavior.

My hope is that Jeffrey Novitzky can get to the bottom of all this. If he does, we will learn that either Landis is an evil monster who is bent on hurting his friends and colleagues by crafting wild tales or that Lance has built his fame and fortune on a massive fraud. Currently, Novitzky doesn’t just have Landis’s story as evidence but many other stories and a history of decades of drug abuse in cycling that seem consistent with, at least some of, what Landis is saying.

In the end, I’ve come to the conclusion that we each need to believe one of two things about Lance Armstrong. That is, either: 

1. Lance is an incredible freak of nature who could beat his rivals even though they were found to be doping, or 
2. Lance's fame and fortune is built on a massive and clever fraud.

I suspect that even if Novitzky were to build an incredible case against Lance and convict him of fraud there would be many who would deny his guilt just as there are probably some who still believe O.J. Simpson is innocent. On the other hand, even if Novitzky fails to provide sufficient evidence for a conviction, there will be some who will believe Lance has shown enough character flaws and enough evidence has been brought forward to determine that he is guilty. This will not be the first fraud case that had these features. Or the last...