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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%

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 8y 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 8y 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 8y 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 8y 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.
    - QuotedForTruth 8y ago
      Did you make a bad deal if the other party reneges? If you pay someone for something and they don't deliver was that you making a bad deal? No way! The weaker/winning rider offered the deal. It was mutually beneficial. If they fight, they likely get caught and neither gets 1st or 2nd. If they make a deal and cooperate, the stronger/losing rider would get 1st and the weaker/winning rider would get 2nd. I don't think that's a bad deal for either rider. To then break the deal is where the problem is. The weaker/winning rider would have had no shot to win without lying first. Thats unsportsmanlike in a sport where these deals are considered ok (which they are).
      - hammock 8y ago
        I hear you. If both riders held up their end, it would have been mutually beneficial. But by "bad deal" I mean, notwithstanding the deal being mutually beneficial, there was really no reason for the weaker rider not to defect and sprint at the end. In OP story, the stronger rider is expecting to finish first. Contrast that with the case you described in parent comment, wherein the stronger (GC) rider is expecting to finish second under the terms of the deal. Very different setup.
- stouset 8y ago
  If they cooperate fully, Rider A has the strongest chance of winning the race. If Rider A defects, he has a lesser chance of winning the race. If Rider A cooperates and Rider B defects, Rider A has the worst possible chance to win the race. I’m not sure how you see this as being a better situation for Rider A. Note that in my example I am, for the sake of simplicity, assuming a single race and am not talking about a stage race where one rider might be stronger but would happily agree to take second because the stage win is of lesser value than the overall time. When I refer to a stronger rider, I mean one who has a solid chance of holding off the pack solo, whereas the weaker rider would almost certainly be unable to be. When the two reach the finish line, I assume they would be reasonably well-matched for a sprint, just for the sake of providing a simple example. In reality, it’s rarely so clear. But if someone knows that cooperating and getting second place is a better result for them in practice than fighting tooth and nail for first and potentially throwing it all away, they’ll make this kind of offer. Likewise if the other cyclist strongly values first place but thinks it’s too risky to cooperate with someone who might be try to snatch victory away at the finish line with a sprint, they’ll be relieved to hear the other person give this offer. Making this offer and reneging is considered poor sportsmanship, and it rarely happens because (presumably) racers expect that doing so will prevent them from being trusted to cooperate in the future.

hammock 8y 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 8y 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 8y 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 8y 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.
  - QuotedForTruth 8y ago
    Did you make a bad deal if the other party reneges? If you pay someone for something and they don't deliver was that you making a bad deal? No way! The weaker/winning rider offered the deal. It was mutually beneficial. If they fight, they likely get caught and neither gets 1st or 2nd. If they make a deal and cooperate, the stronger/losing rider would get 1st and the weaker/winning rider would get 2nd. I don't think that's a bad deal for either rider. To then break the deal is where the problem is. The weaker/winning rider would have had no shot to win without lying first. Thats unsportsmanlike in a sport where these deals are considered ok (which they are).
    - hammock 8y ago
      I hear you. If both riders held up their end, it would have been mutually beneficial. But by "bad deal" I mean, notwithstanding the deal being mutually beneficial, there was really no reason for the weaker rider not to defect and sprint at the end. In OP story, the stronger rider is expecting to finish first. Contrast that with the case you described in parent comment, wherein the stronger (GC) rider is expecting to finish second under the terms of the deal. Very different setup.
stouset 8y ago
If they cooperate fully, Rider A has the strongest chance of winning the race. If Rider A defects, he has a lesser chance of winning the race. If Rider A cooperates and Rider B defects, Rider A has the worst possible chance to win the race. I’m not sure how you see this as being a better situation for Rider A. Note that in my example I am, for the sake of simplicity, assuming a single race and am not talking about a stage race where one rider might be stronger but would happily agree to take second because the stage win is of lesser value than the overall time. When I refer to a stronger rider, I mean one who has a solid chance of holding off the pack solo, whereas the weaker rider would almost certainly be unable to be. When the two reach the finish line, I assume they would be reasonably well-matched for a sprint, just for the sake of providing a simple example. In reality, it’s rarely so clear. But if someone knows that cooperating and getting second place is a better result for them in practice than fighting tooth and nail for first and potentially throwing it all away, they’ll make this kind of offer. Likewise if the other cyclist strongly values first place but thinks it’s too risky to cooperate with someone who might be try to snatch victory away at the finish line with a sprint, they’ll be relieved to hear the other person give this offer. Making this offer and reneging is considered poor sportsmanship, and it rarely happens because (presumably) racers expect that doing so will prevent them from being trusted to cooperate in the future.