Decision Making with a Fixed Reference Point I Pope and Schweitzer (2011) found

Question

Decision Making with a Fixed Reference Point I Pope and Schweitzer (2011) found that professional golfers also display loss aver- sion In golf, there is a fixed reference point for each hole, which is referred to as par. The goal of golf is to finish each hole in as few strokes as possible independent of the value of par. Suppose a golfer can either be aggressive or conservative on each of his putts The probability distribution of the number of putts needed to finish the hole is: One Putt Two Putt Three Putt Aggressive Conservative 10 Suppose the reference dependent utility of PGA Tour golfers is where s denotes the total number of strokes a golfer takes on a hole, and p denotes the par of that hole. aggressive or conservative with his putts? a. If -0, should a golfer be b. Suppose par is 4, and a golfer is putting for birdie (his third shot). Show that if (A-4) > 3, then the golfer strictly prefers to be conservative on his putt. Explain this result. c. Suppose par is 4, and a golfer is putting for par (his fourth shot). Is he going to putt aggressively or conservatively d. Draw a graph of the utility and use it to explain the difference in strategy when putting for birdie and for par The setup of this problem is different from Pope and Schweitzer (2011), but hopefully it captures the spirit. For those interested in the paper, you can find it on Moodle course webpage. 2A putt is a shot or stroke on the green, typically a stroke taken just before finishing a hole.

Explanation / Answer

a. For n=0 the golfer must be aggressive as the utility function is -s for any case of relation between no. of strokes (s) and par of the hole (p). i.e. for any par value the golfer will have a chance of finishing the whole in 1,2 or 3putts once he reaches the green (putting area) as there is a probability for each putt. as against probability of 0,1 and 0 for a conservative approach.

b.For a par p ,a birdie is one that will take p-1 strokes.ie. s= p-1. Here the golfer has 2 available strokes to achieveathe par. If he does it in the 3rd stroke it will be birdie. Using the given condition , i.e. n(l-4)>3 i.e. nl>3+4n [ n is eta and l is lambda] in u

if s <= p

for birdie i.e. s=p-1 , u = -3 + n = n-3

for par i.e. s=p , u = -4 +0= -4

Now if the golfer goes with a conservative approach he will get a sure chance of completting at least a par if not a birdie as the probability of two putt is 1. Thus even if he doesnt score a bird with his 3rd shot, he will surely score a par with his 4th shot!

c. par is 4 . The golfer has one shot to achieve the par as it is his 4 th stroke. Now the probability for one putt is 2/5 for aggressive and 0 for conservative. So ofcourse he must have an aggressive approach.

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