# Game Theory Week 1 Quiz Answers

## Game Theory Week 1 Quiz Answers

In this article i am gone to share Coursera Course Game Theory Week 1 Quiz Answers with you..

### Week 1 Quiz Answers

Question 1)

Find the strictly dominant strategy:

• a;
• b;
• c;
• d;
• x;
• y;
• z

Question 2)

Find a very weakly dominant strategy that is not strictly dominant.
• c;
• x;
• d;
• a;
• y;
• b;
• z

Question 3)

When player 1 plays d, what is player 2’s best response:
• Only x
• Only y
• Only z
• Both y and z

Question 4)

Find all strategy profiles that form pure strategy Nash equilibria (there may be more than one, or none):

• (b, y);
• (d, y);
• (b, z);
• (a, y);
• (c, x);
• (c, y);
• (a, x);
• (b, x);
• (a, z);
• (d, z).
• (c, z);
• (d, x);

Question 5)
There are 2 players who have to decide how to split one dollar. The bargaining process works as follows. Players simultaneously announce the share they would like to receive s_1s1​ and s_2s2​, with 0≤s_10≤s1​, s_2≤1s2​≤1. If s_1+s_2≤1s1​+s2​≤1, then the players receive the shares they named and if s_1+s_2>1s1​+s2​>1, then both players fail to achieve an agreement and receive zero. This game is known as `Nash Bargaining’.

Which of the following is a strictly dominant strategy?

• 1;
• 0.5;
• 0;
• None of the above.

Question 6)
There are 2 players who have to decide how to split one dollar. The bargaining process works as follows. Players simultaneously announce the share they would like to receive s_1s1​ and s_2s2​, with 0≤s_10≤s1​, s_2≤1s2​≤1. If s_1+s_2≤1s1​+s2​≤1, then the players receive the shares they named and if s_1+s_2>1s1​+s2​>1, then both players fail to achieve an agreement and receive zero.

Which of the following strategy profiles is a pure strategy Nash equilibrium?

• (1.0, 1.0);
• (0.3, 0.7);
• (0.5, 0.5);
• All of the above

Question 7)
Two firms produce identical goods, with a production cost of c>0c>0 per unit.

Each firm sets a nonnegative price (p_1p1​ and p_2p2​).

All consumers buy from the firm with the lower price, if p_1≠p_2p1​​=p2​. Half of the consumers buy from each firm if p_1=p_2p1​=p2​.

D is the total demand.

Profit of firm ii is:

• 0 if p_i>p_jpi​>pj​ (no one buys from firm ii);
• Dfrac{p_i−c}{2}D2pi​−c​ if p_i=p_jpi​=pj​(Half of customers buy from firm ii);
• D(p_i−c)D(pi​−c) if p_i<p_jpi​<pj​ (All customers buy from firm ii)

Find the pure strategy Nash equilibrium:

• Firm 1 sets p=0p=0, and firm 2 sets p=cp=c.
• Both firms set p=cp=c.
• Both firms set p=0p=0.
• No pure strategy Nash equilibrium exists.

Question 8)
Three voters vote over two candidates (A and B), and each voter has two pure strategies: vote for A and vote for B.

When A wins, voter 1 gets a payoff of 1, and 2 and 3 get payoffs of 0; when B wins, 1 gets 0 and 2 and 3 get 1. Thus, 1 prefers A, and 2 and 3 prefer B.

The candidate getting 2 or more votes is the winner (majority rule).
Find all very weakly dominant strategies (click all that apply: there may be more than one, or none).
• Voter 1 voting for A.
• Voter 1 voting for B.
• Voter 2 (or 3) voting for A.
• Voter 2 (or 3) voting for B.

Question 9)
Three voters vote over two candidates (A and B), and each voter has two pure strategies: vote for A and vote for B.

When A wins, voter 1 gets a payoff of 1, and 2 and 3 get payoffs of 0; when B wins, 1 gets 0 and 2 and 3 get 1. Thus, 1 prefers A, and 2 and 3 prefer B.

The candidate getting 2 or more votes is the winner (majority rule).
Find all pure strategy Nash equilibria (click all that apply)? Hint: there are three.

• 1 voting for A, and 2 and 3 voting for B.
• 1 and 2 voting for A, and 3 voting for B.
• All voting for A.
• All voting for B.