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Examining Game Theory in Cycling and Why Herrada Wore Red for Two Days

Unbeknownst to likely most of you, La Vuelta a España, the least well-known member of the cycling grand tour triplet, will be finishing soon, with the last stage being on the 16th. In true Vuelta fashion, the race has been less well controlled than other grand tours, allowing for some interesting events, most notably being Jesús Herrada wearing the red jersey (leaders jersey) for two days.

In cycling, the riders can usually be generalized into two groups: the peloton, comprised of most riders or the important ones, and the breakaway, a group that has broken away from the peloton and is ahead on the road. When game theory is talked about in cycling, it’s usually in the context of the prisoner’s dilemma presented to the members of the breakaway. The two options are as follows: sit in behind your opponent and draft, where you save energy, or work, and lose energy but increase the lead the breakaway has on the peloton. In this setup, the dominant strategy for each rider is to sit in and draft. Yet if both riders refuse to work and instead try to sit in each other’s draft, they slow down considerably and are likely to be caught by the peloton. Likely because riders value not being caught over first place, typically riders employ a sort of tit for tat strategy which leads to mutual cooperation and alternating turns of being on the front.

Similarly to how game theory can be applied to the actions of the breakaway, it can also be applied to the actions of the peloton. In this case you have teams, as opposed to riders, but their choices are family similar: sit in and conserve energy, or work and expend energy while at the same time closing in on the break. Bringing this back to Herrada putting on red, this is the situation that occurred out in La Vuelta stage 12. As La Vuelta had been playing out, there were two teams with riders with a strong chance of winning: Michelton-Scott and Movistar. On stage 12, a mountain stage, both teams were reluctant to work and lose energy compared to the other. Instead of either team doing work to catch Herrada once he took the virtual lead, the teams settled into the Nash Equilibrium of neither team doing any work. This allowed Herrada to gain an over 3 minute lead in the general classification, and the breakaway to win by over 11 minutes. Because both the situation of the breakaway and the peloton feature two results to each decision: energy conserved/lost and time gained/lost, which equilibrium is chosen—being mutually cooperative vs. mutually uncooperative–can indicate which the players in a game value most: energy or time. In the case of La Vuelta, Michelton-Scott’s energy saving gambit worked out, and after two days, Simon Yates, the team’s general classification leader, was back in red. Now the real question is can he continue to hold it till Sunday or will he drop the ball like in Il Giro.


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September 2018