Bill and Ted, two teenagers from San Dimas, California, are playing the game of
ID: 1103355 • Letter: B
Question
Bill and Ted, two teenagers from San Dimas, California, are playing the game of chicken. Bill drives south on a one-lane road and Ted drives north along the same road. Each has two strategies: Stay or Swerve. If one player chooses Swerve he looses face; if both Swerve, they both loose face. If both choose Stay, they are both killed. Con- sider the following payoff matrix
a. What is the expression for Bill and Ted’s expected payoffs?
b. What is the breakeven probability? Explain.
c. What is the risk-dominant strategy? Explain.
Bill Stay Swerve Stay 3, -3 2, 0 Swerve 0, 2 1, 1 TedExplanation / Answer
b.) What is the breakeven probability? Explain.
X = TFC / (P - V)
TFC
3*3
9
P
0*0
0
Value(p)
1
1
1,1
2
2,0
1,8
3
-3,-3
3
4
2,5
3,3
5
0
0
p-v
3,3
0
D can’t be -ve
assume its +ve
0
1,1
2
20
c. What is the risk-dominant strategy? Explain.
Before the catastrophic event; U=in (0, 2).
Probability catastrophic events will occur;
(1, 1)(-3,-3)
3
Probability that catastrophic events will not occur
E (u) = 2--3
There is only 5 probability of other catastrophic events to occur and both Ted and Bill get killed; therefore -3,-3 an actuarially fair number for both players to accept to stay and lose their lives and chances are (1, 1) for the risk of choosing a dormant strategy whereby both the players will be made better off and none of them will be made worse off.
X = TFC / (P - V)
TFC
3*3
9
P
0*0
0
Value(p)
1
1
1,1
2
2,0
1,8
3
-3,-3
3
4
2,5
3,3
5
0
0
p-v
3,3
0
D can’t be -ve
assume its +ve
0
1,1
2
20
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