CAS EC 101 Lecture Notes - Lecture 24: Matching Pennies, Demand Curve, Stackelberg Competition

64 views5 pages

yellowlion956

19 Dec 2017

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

tealzebra3 and 39199 others unlocked

CAS EC 101 Full Course Notes

Verified Note

56 documents

Document Summary

Vanesa moves first: she buys a ticket either for the football match or for the opera. She shows miguel her ticket, so he knows what she has done. Then miguel moves: he buys his ticket either for the football match or for the opera. Cq: if vanesa moves first, what is true about : it is a nash equilibrium b) vanesa would deviate c) miguel would deviate d) none of the above. Yes, r, always r is a nash equilibrium, but it will not occur if both players are rational. This is because always r is not time-consistent, and a rational miguel would not follow it during the game and vanesa knows he won"t. So, if vanesa moves first, she will choose f , even if miguel says he will follow always r . To show this, we need a different model of the game: the extensive-form game.

Related Questions

Consider the infinitely repeated game of Prisoners Dilemma that has the following payoff structure. Each player has a discount rate r. Suppose both players are using the Tit-For-Tat strategy.

		Column
		Defect	Cooperate
Row	Defect	2, 2	10, 1
	Cooperate	1, 10	6, 6

(a) Under what condition does a player have an incentive to deviate once from cooperating and then revert to it? [4 points]
(b) Under what condition does a player have an incentive to deviate from cooperating forever? [4 points]
(c) Under what condition is it a Nash equilibrium that both players use the Tit-For-Tat strategy? [2 points]

ceruleangnat915

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:
Player A: LEFT RIGHT
TOP 2 5 | 1 4
BOTTOM 0 1 | 3 8

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

bluelouse209

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).

PrisonerÃ¢â¬â¢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 1Ã¢â¬â¢s best response function (choice of p as a function of q), and player 2Ã¢â¬â¢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 ÃÂ± 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 personÃ¢â¬â¢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 (ÃÂ±)			Player 2 is weak (1-ÃÂ±)			Player 2 is strong (ÃÂ±)

After writing all the strategies and payoffs in the same matrix, find the Bayesian Nash equilibriums, depending on the value of ÃÂ± (ÃÂ± Ã¢â°Â¤ 1/2 or ÃÂ± Ã¢â°Â¥1/2).

jadebuffalo465

CAS EC 101 Lecture Notes - Lecture 24: Matching Pennies, Demand Curve, Stackelberg Competition

CAS EC 101 Full Course Notes

Document Summary

Get access

Related Documents

CAS EC 101 Lecture Notes - Lecture 24: Matching Pennies, Stackelberg Competition, Subgame

CAS EC 101 Lecture Notes - Lecture 23: Matching Pennies, Delta Air Lines, Nash Equilibrium

CAS EC 101 Lecture Notes - Lecture 21: Nash Equilibrium, Coordination Game, Solution Concept

Related Questions