ECON 221 Chapter Notes - Chapter 4-6: Nash Equilibrium, Pennsylvania Route 56, Uuencoding

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pinkmole815

21 Oct 2015

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There are six pure-strategy nash equilibria, each of which entails the two players choosing the same letter. Any equilibrium could be focal, depending on the underlying common cultural understandings of the two players; to achieve a focal equilibrium, their expectations must converge. In a society that emphasized the importance of being first, (g, g) might be focal. If the society valued equality above all else, (q, q) would be focal because it gives equal payoffs to the two players. In an environment in which people cared about the total social welfare, (l, l) would be focal because it maximizes total payoff. There are six pure-strategy nash equilibria: (yellow, lavender, black), (lavender, yellow, Black), (black, yellow, lavender), (yellow, black, lavender), (lavender, black, yellow), and (black, Dtc"s profit is ydtc = pqdtc 12qdtc = (120 qdtc)qdtc 12qdtc = qdtc. The profit-maximizing quantity for dtc is qdtc = 54.

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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

AI 16. If the price of X is set at $0.10 per unit, the quantity of the good purchased by this consumer each month will be: B) 2 C)3 D) 4 E) 6 F) 8 G) 10 H) 12 I) 16.5 J) 23.5 K) 63 L) 64 M) 128 N) 129 0) 150 P) 156 Q) 157.5 R) 159.5 S) 160 T) 255 U) 256 V) 256.5 W) 257.5 X) 260 Y)0 Z) none of the above

22. A market is in equilibrium at the point P = $100, Q = 6000. You are told that at that point, the elasticity of demand is 1.2 (or 6/5) and the elasticity of supply is 3.6 (or 18/5). If a $1 per unit tax is placed on consumers in this market, then you know that the fraction of the tax (rounded to the nearest two decimal places) that falls on consumers (buyers) will be: A)0 B) 0.05 C) 0.10 D) 0.15 E) 0.17 F) 0.20 G) 0.25 H) 0.30 1) 0.33 J) 0.40 K) 0.42 L) 0.50 M) 0.54 N) 0.60 0) 0.65 P) 0.67 Q) 0.70 R) 0.75 S) 0.80 T) 0.83 U) 0.85 V) 0.90 W) 0.95 X) 1 Y) 0.77 Z) none of the above

ECON 221 Chapter Notes - Chapter 4-6: Nash Equilibrium, Pennsylvania Route 56, Uuencoding

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