QUESTION 35 Bonus: The following question is a football scenario. Although this may be of interest to many of you, knowledge of the sport is uncessesary to answer this question. Althought that is needed is a basic knowledge of game theory. The Patriots are up by 2 points against the Jets with 10 seconds remaining. It is fourth down with fifteen yards to go on the New England 10 yard line. Neither team has any time outs and the coaches need to determine the plays that are most likely to succeed. The Patriots will either decide to punt or fake a punt to convert a first down. If the Patriots convert a first down, they will be able to run out the clock and win the game. If they are able to punt down field without a punt return from the Jets, most of the time will be exhausted. the Jets would be out of field goal range. However, if the Patriots fake a punt and fail to convert a first down, the Jets would easily be able to win the game with a short field goal. At the same time, if the Jets are able to return the punt, they will likely be in range for a long field goal. These screnarios depend on what the Jets decide to do on defense. The Jets can either keep two or three returners deep, or they can play tighter defense to protect the pass. Patriots Punt Fake Punt Guard Pass -2, 2 3,-3 Jets Return Punt 3,-3 -2,2 Patriots will punt if they think that the Jets will guard the pass with greater than 50 percent probability The Jets will return the punt if they think the probability that the Patriots will be punt is greater than 50 percent Patriots will punt if they think that the Jets will guard the pass with less than 50 percent probability