Coursera Answers

Game Theory Week 1 Quiz Answers

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:


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.



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:


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):

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.