Consider the choices made by Athlete A and Athlete B, two college athletes set to play each other. Their optimal choice would be to both rest. Let us assume that the outcome of the game, in terms of wins, would be the same as the outcome would be if they both exert extra effort (due to equal marginal benefits of training). In either case, they would tie or have similar expected win probabilities. However by jointly exerting less effort, they are better off (the same payoff, but less cost).
If one player rested while the other trained, the player who put in extra effort would be better off because they would do better (win more) than they would in either the effort/effort scenario or the rest/rest scenario. The extra effort (extra cost) would be worth it. On the other hand, the player who rested would be worse off because even though they exerted less effort (lower cost), their payoff would be lower because they would have a much lower win payoff.
While the ideal individual scenario for you as an athlete is to exert the extra effort to win while your opponent rests, the nash equilibrium is for both players to exert extra effort, leaving them with the same payoff as they would have if they both rested, but with the added costs of training. The nash equilibrium, from both players playing their dominant strategies, is not Pareto optimal. Thus, this is a prisoner’s dilemma.
1 comment:
As a student-athlete, I can attest to the article stating the amount of time I put into my sport per week well exceeds the 20-maximum used for official practices with coaches. Being an athlete is no different from being a student; the number of hours you put in determines how successful you will be. The 20 hours per week seems like a lot as it is, but there is always something that you can do to improve yourself or better prepare yourself for a competition. It is very exhausting, but it is very rewarding. The results do not lie.
I really enjoyed reading this article especially since I can relate to it, but I also like it because I find it interesting to look at my sport in terms of economics. There are a lot of things that I agree with, and I really believe that there can definitely be instances where it’d be more efficient for both of the players to choose to not try in order to get the result that they desire without exerting all the effort (they can save it for another time/competition). With that being said, I also think that the prisoner’s dilemma game can also be improved. I believe that there is moment where the pareto efficient outcome would be both players exerting a lot of effort, and I believe that more elements can be added to the game to greater understand the results of competitions.
Going against the grain a bit, I think that there are instances where exerting a lot of effort is pareto efficient for both of the athletes. One of the common phrases in the NBA is saying someone is “In midseason form” meaning the work they put in at the beginning of the year is really starting to show. I think that the many college sports are no different to the NBA in this instance showing that it’d make sense to put in a lot of effort in order to be stronger and better later on down the road when the athletes begin to taper. Because the end of the year is more important than the beginning, it’d make sense for all the teams to choose to put a majority of the work in at the beginning of the year. As for elements that can be added, I think that there are multiple stages to the prisoner’s dilemma per competition. Thinking to UVA basketball, each half is its own prisoner’s dilemma. The first half UVA may choose max effort, but in the second half, maybe the effort is not necessary because the game is already in the bag. With multiple stages, we also can get varying degrees of effort as well.
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