Question 1

Hamilton and Virginia have two strategies each a their disposal: top and bottom. For the strategy combination (top, top)the payoff is (60,20), where the first position refers to Hamilton, and the second to Virginia. Similarly, for (top, bottom)the payoff is (0, 0), for (bottom, top)the payoff is (0, 0), while for (bottom, bottom)is (20, 60). What is the mixed strategy equilibrium for this one- shot game?

Accepted Answer

The answer of Hamilton and Virginia have two strategies each...

Question 2

Fergie and Abdul were caught by the police in the vicinity of a robbery site. The police have a strong feeling the two individuals are the actual robbers, but they do not have a way to prove it yet. In the absence of hard evidence, the prosecutor can convict them of only a minor offence, with only a year in prison. The police put the two in separate rooms and try to offer them incentives to confess: if one of the robbers does so, he would go
scot- free while the other goes to prison for 10 years. If both confess the prosecutor will be able to put both in prison for 5 years. As a result, each partner in crime has two options: to confess or to remain silent.
Note: here payoffs are in years of prison, so less is better.
a)Represent this game in normal form. Are there dominant strategies for these robbers?
b)What s the Nash equilibrium of this game?
c)How is this game called?
d)What exactly is the dilemma that the two robbers have? Is there a way to get around this problem

Accepted Answer

The answer of Fergie and Abdul were caught by the...

Question 3

Maya and Allen contemplated going to one of the two parties their school buddies organize that night. Just before deciding what party to attend, Allen's cell phone went dead. Now they have to come up with a way to find each other. In their minds, it was as if they play the following game. Each has a choice between two parties, the big one and the small one. The payoffs are as follows: for the strategy combination (big, big)the payoff is (200,200), where the first position refers to Maya, and the second to Allen. Similarly, for (big, small)the payoff is (0, 0), for (small, big)the payoff is (0, 0), while for (small, small)is (500, 500).
a)Does this game have a dominant strategy Nash equilibrium?
b)What are the two pure strategy equilibria?
c)How is this game referred to among game theorists?
d)Is there an equilibrium that is Pareto superior to the other? If yes, is there a possibility Maya and Allen will choose it?

Accepted Answer

The answer of Maya and Allen contemplated going to one...

Quiz 15: Introduction to Game Theory