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ECON 171 Final: ECON 171 Final Exam Winter 2014

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turquoisegnu128
31 Jan 2019
School
UCSB
Department
Economics
Course
ECON 171
Professor
All

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Document Summary

Final exam, econ 171, march, 2015, with answers. Good luck! (true or false) if a player has a dominant strategy in a. Problem 1. simultaneous-move game, then she is sure to get her best possible outcome in any nash equilibrium of the game. explain your answer and give an example of a game that illustrates your answer. In this game, defect is a dominant strategy for both players. The best possible outcome for either player is for this player to defect and the other player to cooperate. But this outcome is not a nash equilibrium. The only nash equilibrium is one in which both defect. Consider the game represented in the table below, where player 1 chooses the row and player 2 chooses the column. 2,-2: find all of the pure strategy nash equilibrium strategy pro les for this game if t > 0. In one of them player 1 swerves and player 2 does not.

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Related Questions

4. Game theory terminology

Select the term that best describes each definition listed in the following table.

Definition

Nash Equilibrium

Dominant Strategy

Collusion

Tit-for-tat Strategy

Payoff Matrix

Prisoners' Dilemma
A player's best choice, if it exists, regardless of his or her opponent's strategy              
A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents              
A case in which individually rational behavior leads to a jointly inefficient outcome              
A visual representation of a game showing all possible strategies for each player and all potential outcomes and payoffs              

Problem 1

In each of the three games shown below, let p be the probability that player 1 plays cooperates (and 1- p the probability that player 1 defects), and let q be the probability that Player 2 plays cooperates (and 1- q the probability that player 2 defects).

Prisoner’s Dilemma

Player 2

Player 1

cooperate

defect

cooperate

70,70

10,80

defect

80,10

40,40

Stag Hunt

Player 2

Player 1

cooperate

defect

cooperate

70,70

5,40

defect

40,5

40,40

Chicken

Player 2

Player 1

cooperate

defect

cooperate

70,70

50,80

defect

80,50

40,40

1. For each game, draw a graph with player 1’s best response function (choice of p as a function of q), and player 2’s best response function (choice of q as a function of p), with p on the horizontal axis and q on the vertical axis.

2. Using this graphs, find all the Nash equilibriums for the game, both pure and mixed strategy Nash equilibriums (if any). Label these equilibriums on the corresponding graph.

3. In those games that have multiple pure strategy Nash equilibriums, how do the expected payoffs from playing the mixed strategy Nash equilibrium compare with the payoffs from playing the pure strategy Nash equilibriums? Which type of strategy (mixed or pure) would players prefer to play in these games?

Problem 2

Two people are involved in a dispute. Player 1 does not know whether player 2 is strong or weak; she assigns probability α to player 2 being strong. Player 2 is fully informed. Each player can either fight or yield. Each player obtains a payoff of 0 is she yields (regardless of the other person’s action) and a payoff of 1 if she fights and her opponent yields. If both players fight, then their payoffs are (-1; 1) if player 2 is strong and (1;-1) if player 2 is weak. The Bayesian game is the following, depending on the type of player 2:

Y

F

Y

F

Y

0, 0

0, 1

Y

0, 0

0, 1

F

1, 0

-1, 1

F

1, 0

1, -1

Player 2 is strong (α)

Player 2 is weak (1-α)

Player 2 is strong (α)










After writing all the strategies and payoffs in the same matrix, find the Bayesian Nash equilibriums, depending on the value of α (α ≤ 1/2 or α ≥1/2).



Suppose that two players are playing the following game. Player A can choose either Top or Bottom, and Player B can choose either Left or Right. The payoffs are given in the following table:



Where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.

A) (1 point) Does player A have a dominant strategy, and if so what is it?

B) (1 point) Does player B have a dominant strategy and if so what is it?

C) (4 points) For each of the following say true if the strategy combination is a Nash equilibrium, and false if it is not a Nash equilibrium:

i) Player A plays Top and Player B plays Left

ii) Player A plays Bottom and Player B plays Left

iii) Player A plays Top and Player B plays Right

iv) Player A plays Bottom and Player B plays Right

D) (2 points) If each player plays her maximin strategy what will be the outcome of the game? (Give your answer in terms of the strategies each player chooses)