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.