Behavior Strategic Spring 2011
Homework Assignment 2
Due: Wednesday, February 15, 2011
This homework assignment is based on the material in chapters 2 and 3 of the course text
(Harrington). Please ensure your assignment is legible.
1.
(Question 6, chapter 2) Consider a contestant on the game show Lets Make a Deal. There
are three doors, and behind two of the doors is a prize of little value, while behind one
door is a prize of considerable value. The doors are labeled 1, 2, and 3. The strategic
situation starts when, prior to the show, the host selects one of the three doors behind
which to put the good prize. Then, during the show, a contestant selects one of the three
doors. After its selection, the host opens one of the two doors not selected b y the
contestant. In opening a door, a rule of the show is that the host cannot open the door
with the good prize. After the host opens a door, the contestant is then given the
opportunity to continue with the door originally selected or switch to the ot her unopened
door. After the contestants decision, the remaining two doors are opened.
2.
(Question 8, chapter 2) For the extensive form game below, derive the corresponding
strategic form.
1
a1
b1
2
0
0
a2
b2
10
5
1
c1
d1
2
c2
d2
c2
5
2
15 20
03
d2
4
1
3.
(Question 8, chapter 3) Consider the three-player game shown in the figure below. Player 1
selects a row, either a1, b1 or c1. Player 2 selects a column, either a2 or b2. Player 3
selects a matrix, either a3 or b3. The first number in a cell is player 1s payoff, the second
number is player 2s payoff, and the last number is player 3s payoff. Derive the strategies
that survive the iterative deletion of strictly dominated strategies.
Player 3a
Player 3b
Player 2
Player1
a1
b1
c1
4.
Player 2
a2
3,1,0
b2
2,3,1
0,3,1
1,0,2
1,1,0
1,2,1
Player 1
a1
b1
c1
a2
3,1,1
b2
1,3,2
2,0,2
1,1,1
2,2,1
0,2,0
Model in extensive form the final minutes of the Super Bowl game, played February 5,
2012. A brief synopsis follows.1 Include any additional necessary details to ensure your
model is complete (including payoffs).
They got some help from Patriots coach Bill Belichick, whose late-game risk didn't turn out as
he planned. Belichick reasoned the Giants would run the clock down and kick a short field goal,
so he gambled by allowing the six points. The ploy failed. "Ball was inside the 10-yard line, a 90
percent field goal conversion," he said." Manning did everything asked of him in the final
minutes, a habit for the eight-year veteran. It was a classic I-can-top-that showdown with the
outcome in doubt until the last desperation pass fell to the turf as the last second ticked off the
clock.
Eli Manning engineered his second fourth-quarter comeback in as many Super Bowl
appearances and it was eerily similar to his first one four years ago. He showed that brilliance
in the clutch on the winning drive, completing five passes, starting with a sensational 38 -yard
sideline catch by Mario Manningham. On second down at the Patriots 6 and with only one
timeout remaining, Belichick had his defense stand up as Bradshaw took the handoff. Bradshaw
thought about stopping short of the end zone, then tumbled in untouched. "I was yelling to
him, 'Don't score, don't score,' " Manning said. "He tried to stop, but he fell into the end zone."
Brady couldn't answer in the final 57 seconds, although his heave into the end zone on the final
play fell just beyond the grasp of lunging All-Pro tight end Rob Gronkowski.
1
From http://espn.go.com/nfl/recap?gameId=320205017, accessed 2/6/2012.
5.
Convert your extensive form model from question 4 above. to strategic form.
6.
What do you find to be the most difficult concept presented in class to date? Please
explain in at least two sentences, more if it would help to clarify the issue. (i.e., I find
determining players to be the most difficult concept. This is because I cannot decide if a
player who only sometimes gets to play is allowed to be in the game.)
.