Prisoner’s Major Baseball League or Lance Armstrong, there

Prisoner’s dilemma happens all the time in the real world. One example is in sports and doping. Wether its cycling, boxing, the Major Baseball League or Lance Armstrong, there have been many incidents of steroid use. Usually, people who cheat in such situations is because it happens ot be their optimal strategy since the risk of punishment is high. Furthermore, often times people who use steroids report doing so because they thought other’s were also doing it. In this situation there are 4 outcomes:Outcome 1- Nobody uses steroids which is preferable because it allows sports to be played fairlyOutcome 2 and 3- One group uses steroids and the other doesn’t. Which means that one group will have an advantage. Thus, to level the playing field, the other group that did not cheat is pressured to cheat. Giving us outcome 4:Outcome 4- Everyone uses steroids. Using steroids is a dominant strategy because when others don’t use them you gain an advantage and when they do you simply level out the playing field. However in outcome 4, everyone ends up worse than in outcome 1. Since everyone is taking drugs in outcome 4 the average level of competition increases and no one has an advantage, however they have to deal with the negative health effects of steroids plus the risk of getting punished by sports organizations. Unfortunately the Nash equilibrium points to outcome 4 due to everyone’s dominant strategy to use steroids.And though it is morally wrong to use steroids we can see why athletes feel pressured to use them.To stop the Nash equilibrium society has to find a way to make steroid use not a dominant strategy.  One way could be to increase the risk of punishment and the level of punishment until it is not favorable to use steroids. However, if this doesn’t work, society will need to find another way to prevent people from steroid use.The consequences to defecting or cooperating are certain hours in detention. If Douceline defects against Mariika, while Mariika cooperates,Douceline that lied doesn’t have to spend any hours in detention and Mariika that told the truth gets 10 hours in detention. If both students tell the truth then each will serve a six hour time in detention. If they both defect then they both serve 5 hours.   To find the expected value we will look at prisoner’s dilemma through Douceline’s point of view since in the end they both have the same expected value Define variables:x= The probability that Douceline defectsy= probability that Mariika defectsz= Douceline’s expected value ? E(Z)