Answered: The deciding shot in a soccer game…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

For the following questions consider this setting.

The deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the striker shots the ball in the other, then it is a goal. If the goalie jumps left and the striker shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the striker shots right, it is goal with probability 2/3.

QUESTION Say the goalie's strategy is to jump left with probability 1 and the striker shoots left with probability 0.5, then the probability of a goal is (round to two digits)

QUESTION If the striker shoots in either corner with probability 0.5 and the goalie likewise shoots in either corner with probability 0.5, then the probability of a goal is (round to 2 digits)

You can write the probability of a goal as follows:
π(p, s)
=
digits)
X+Y(p+s) - s * p
where pi refers to the probability of a goal, s refers to the probability that the striker
shoots left, and p refers to the probability that the goalie jumps left. X is a number.
What is this number? (round to 2 digits)
Similarly, what is the value of Y (round to 2

If both players play Nash strategies, what is the expected value of goals that will
follow from this penalty shot.
0
1/9
2/9
3/9
4/9
5/9
6/9
7/9
8/9
1

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