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I realize you already know this, but just to add to what you've said... It also makes a lot more sense in stage races. The win for the day's stage is not the

I realize you already know this, but just to add to what you've said... It also makes a lot more sense in stage races. The win for the day's stage is not the only win to be had. The overall race win is based on combined time across all stages. Often someone who is in the running for the overall race win will make a deal with someone who isn't. By not attacking each other, their average speed can be higher. One rider gets to win the stage and the other gets the benefit of working together to finish the stage in the quickest possible time. This allows them to gain on their rivals for the overall win. In a single stage race, the win is mostly the only thing that matters.

hammock 7y ago
In that case aside from missing a stage win, it really doesn't hurt the stronger rider at all when the weaker rider defects. Wouldn't call that a prisoner's dilemma.
- stouset 7y ago
  Of course it does. Assume Rider A believes (rightly) that they're stronger in the break than Rider B. If they don't bring Rider B along, they might have a 50% chance of making first place and a 50% chance of getting caught and losing in a bunch sprint (time-trialists don't generally make good sprinters and vice versa). If they do bring Rider B along, but Rider A does more work (perhaps Rider B is holding back a little bit, knowing they will try to steal the first-place finish) they might have an improved 75% chance of staying away from the pack but there's a 50% or greater chance that Rider B will sprint and win the finish. If they cooperate, Rider A has a 75% chance of first place and Rider B has a 75% chance of second place, with both having a 25% chance of a pack finish. If Rider A defects, Rider A has a 50% chance of a first-place finish and Rider B has a 0% chance of a podium finish. If Rider B defects, both Rider A and Rider B have a 37.5% chance of a first-place finish and a 75% chance of getting a podium. If Rider B values a 75% chance of second place higher than a 37.5% chance of a first place finish, they'll offer this deal. Note that this isn't strictly a Prisoner's Dilemma becuase there's no concept of a double-defection: if Rider A defects, Rider B won't have a chance to. Obviously in a real-world situation you won't know these percentages, but hopefully it illuminates how both sides benefit from cooperation but lose if they want to cooperate and but the other side defects.
  - hammock 7y ago
    Sorry I'm not following the way you laid it out. Here simply is how I think of it: A deal is made. If the weaker rider defects and wins the stage (as in OP story), the stronger rider still has a better time than he would have without the deal - thereby reducing his overall total time for the multi-stage race. The only thing he has to avoid (obviously) is making a deal with the SAME weaker rider for every stage.
    - TeMPOraL 7y ago
      If the stronger rider doesn't care about their podium position, he won't lose much because of the weaker driver defecting. But if he does care, then he does lose.
    - QuotedForTruth 7y ago
      I think you have the riders confused. The rider going for the overall win (general classification or GC rider) would be the one agreeing to not go for the stage. He may be the stronger rider with a 90% chance to win the stage in an all out battle. But, since the race win is much more prestigious than any one stage, he may value the potential time gains over that 90% chance of a stage win and agree to give it up. The defector would then be this GC rider deciding to take the stage win AND the time gains. This leaves the other with only time gains which he may not value at all since he is not in contention for the overall race. In grand tours like the Tour de France or Giro d'Italia, 95% of the riders have no hopes of winning the entire race. They are there to help their teammates who do have a shot and/or attempt to win individual stages. Because of this they often lose lots of time on stages they aren't going to win and thus don't care about winning some trivial amount back.
      - hammock 7y ago
        Ok that makes sense. Then, in the OP story, isn't the guy who won the weaker rider? So the type of deal we're talking about here is irrelevant - the stronger rider just made a bad deal.
        7y ago
- usrusr 7y ago
  Winning without a deal is preferable to winning with a held deal, which is preferable to winning with a broken deal which may or may not be preferable to getting caught by the chasers die to lack of a deal (or due to a weakly trusted one). A similar hierarchy can be made for a stronger rider in a stage race who has a time preference (over points) and who therefore grants the stage win: granting without an explicit deal is a better investment in future cooperation prospects than an explicit deal (because it can influence all future co-breakists), an explicit deal is preferable to coming in second due to being weaker, which is still greatly preferable to getting caught by the chasers.
stouset 7y ago
> In a single stage race, the win is mostly the only thing that matters. You're right that this happens mostly in stage races, but it definitely happens in single-stage races too! If a rider is trying to get a category upgrade—say to Cat 1—they might make this offer knowing that it will help them get over the threshold even if they don't get first. Especially if they know they need these points in the next few races, they might make this deal rather than take the risk of not getting enough to qualify.

hammock 7y ago

In that case aside from missing a stage win, it really doesn't hurt the stronger rider at all when the weaker rider defects. Wouldn't call that a prisoner's dilemma.

stouset 7y ago
Of course it does. Assume Rider A believes (rightly) that they're stronger in the break than Rider B. If they don't bring Rider B along, they might have a 50% chance of making first place and a 50% chance of getting caught and losing in a bunch sprint (time-trialists don't generally make good sprinters and vice versa). If they do bring Rider B along, but Rider A does more work (perhaps Rider B is holding back a little bit, knowing they will try to steal the first-place finish) they might have an improved 75% chance of staying away from the pack but there's a 50% or greater chance that Rider B will sprint and win the finish. If they cooperate, Rider A has a 75% chance of first place and Rider B has a 75% chance of second place, with both having a 25% chance of a pack finish. If Rider A defects, Rider A has a 50% chance of a first-place finish and Rider B has a 0% chance of a podium finish. If Rider B defects, both Rider A and Rider B have a 37.5% chance of a first-place finish and a 75% chance of getting a podium. If Rider B values a 75% chance of second place higher than a 37.5% chance of a first place finish, they'll offer this deal. Note that this isn't strictly a Prisoner's Dilemma becuase there's no concept of a double-defection: if Rider A defects, Rider B won't have a chance to. Obviously in a real-world situation you won't know these percentages, but hopefully it illuminates how both sides benefit from cooperation but lose if they want to cooperate and but the other side defects.
- hammock 7y ago
  Sorry I'm not following the way you laid it out. Here simply is how I think of it: A deal is made. If the weaker rider defects and wins the stage (as in OP story), the stronger rider still has a better time than he would have without the deal - thereby reducing his overall total time for the multi-stage race. The only thing he has to avoid (obviously) is making a deal with the SAME weaker rider for every stage.
  - TeMPOraL 7y ago
    If the stronger rider doesn't care about their podium position, he won't lose much because of the weaker driver defecting. But if he does care, then he does lose.
  - QuotedForTruth 7y ago
    I think you have the riders confused. The rider going for the overall win (general classification or GC rider) would be the one agreeing to not go for the stage. He may be the stronger rider with a 90% chance to win the stage in an all out battle. But, since the race win is much more prestigious than any one stage, he may value the potential time gains over that 90% chance of a stage win and agree to give it up. The defector would then be this GC rider deciding to take the stage win AND the time gains. This leaves the other with only time gains which he may not value at all since he is not in contention for the overall race. In grand tours like the Tour de France or Giro d'Italia, 95% of the riders have no hopes of winning the entire race. They are there to help their teammates who do have a shot and/or attempt to win individual stages. Because of this they often lose lots of time on stages they aren't going to win and thus don't care about winning some trivial amount back.
    - hammock 7y ago
      Ok that makes sense. Then, in the OP story, isn't the guy who won the weaker rider? So the type of deal we're talking about here is irrelevant - the stronger rider just made a bad deal.
      - 7y ago
usrusr 7y ago
Winning without a deal is preferable to winning with a held deal, which is preferable to winning with a broken deal which may or may not be preferable to getting caught by the chasers die to lack of a deal (or due to a weakly trusted one). A similar hierarchy can be made for a stronger rider in a stage race who has a time preference (over points) and who therefore grants the stage win: granting without an explicit deal is a better investment in future cooperation prospects than an explicit deal (because it can influence all future co-breakists), an explicit deal is preferable to coming in second due to being weaker, which is still greatly preferable to getting caught by the chasers.

stouset 7y ago

> In a single stage race, the win is mostly the only thing that matters. You're right that this happens mostly in stage races, but it definitely happens in single-stage races too! If a rider is trying to get a category upgrade—say to Cat 1—they might make this offer knowing that it will help them get over the threshold even if they don't get first. Especially if they know they need these points in the next few races, they might make this deal rather than take the risk of not getting enough to qualify.