Homework answers / question archive / Question 1          Given a sequential game, G = (N, (s1,……Sn), (U1

Question 1          Given a sequential game, G = (N, (s1,……Sn), (U1

Economics

Share With

---

Question 1         

Given a sequential game, G = (N, (s1,……Sn), (U1..Un)  write down the formal definition of subgame perfect. Nash equilibrium strategy profile.

 

Question 2

Consider the following situation: Player 1 is the head of the sports ministry and player 2 is running for the presidency of that country's soccer federation. Suppose that 2 odds of winning the election of the soccer federation is quite high but player 1 does not like him, and does not want to see him as the president of the soccer federation. Player 1 moves first and announces whether or not player 2 should run for the election. Player 1 has two choices, he can announce that player 2 should not enter the election or stay silent. Player 2 Observe. Player 1's action and based on that can choose to announce his candidacy or stay out of the elections. If player 1 chooses player 2 should not run for election' action and player 2, stays out of the election' the resulting payoff are 4 for player 1 and 1 for playa 2. However if player 2 'runs for presidency' when player 1 has chosen player 2 should not run for election, strategy,   are 5 to player 1 and 1 to player, 2 when player 2 awaits "'stay out of the election, strategy. Finally. for the case when if player 1 chooses stay silent' action and playa 2 "run for presidency strategy the payoff are 3 to player 1 and 4 to player 2

  (1) Draw the game three of the above described sequential game.

 (2) Draw the game table and find the set of pure strategy Nash equilibria

 (3) Find the subgame perfect Nash equilibrium of this game. For Nash equilibria which are not subgame perfect, if any, indicate the non-credible threat of player 2.

 

Question 3 (a)

 A child's action a affects both her own private income c(a) and her parent's income p(a); for all values of a we have c(a) < p(a). The child is selfish. She cares only about the amount of money she has. The parent cares both how much money she has and how much her child has. Specifically, parent's payoff is the smaller of the amount of money she has and the amount of money her child has. The parents may transfer money to her child. First the child take an action and after observing the action the parent decides how much money to transfer to the child Show that in the subgame perfect equilibrium of this game the child takes an action that maximizes the sum of private income and her parent's income.

 

Question 4

Find out the set of all (pure and mixed) Nash equilibrium strategy profiles of the follow-ing game. Illustrate each step clearly.

 L                                             Z

Player A              

1,1	2,0
0,2	4,3

Question 5  

Consider a bargaining game where a perfectly divisible total of 100 TL is to be divided between two players. Say Rebecca and Peter. Peter moves first and decides between "si-multaneous" and sequential". It he chooses the former, then each of them tells a money amount for himself (hers...). If the sum of those does not exceed 100, then each of them receives what he/she says. Otherwise, neither of them receives a money. If he chooses the "sequential” then Peter first picks a money amount for himself and then Rebecca observes it, and then he picks an amount for herself. The division rule is the same as above.

1. Draw the game tree
2. Find out the Subgame perfect Nash equilibrium of the game.