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UCLA POLSCI 30 - PS30 Homework 3

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1Cole Chelsea ColePS30Chwe – Discussion Section 1F25 October 2018Homework 31. Recycle a little Recycle a lotRecycle a little 0,0 0,-5Recycle a lot -5,0 10,10The Nash Equilibria are as follows: 0,0 (Recycle a little, Recycle a little) 10,10 (Recycle a lot, Recycle a lot)2. Lie Tell the TruthLie 5,5 -10,0Tell the Truth 0,-10 2,2This game is not an example of a Prisoner’s Dilemma because there are no strategies are stronglydominated. It is standard procedure for police to interview witnesses separately so that they can’t coordinate their stories.The Nash Equilibria are as follows: 5,5 (Lie, Lie) 2,2 (Tell the Truth, Tell the Truth)3. Harrison fights Harrison pretendsWright fights -10,-10 0,-50Wright pretends -50,0 5,5Both Wright and Harrison agreed and intended to pretend fight, but both had suspicions that the other would fight for real which would drastically effect the other’s payoff if the other were to fight and they were to pretend because they would get physically hurt, etc. So, if one suspects theother will fight for real, the more likely they are to fight for real and therefore they both end up fighting for real which ends up giving a payoff much worse compared to that if they had both pretended.4.Chemical Weapons NotChemical Weapons -10,-10 -5,-502Cole Not -50,-5 0,05.Plastic Surgery Stay NaturalPlastic Surgery 10,10 5,-5Stay Natural -5,5 0,06. [q] [1-q] 2 swerves 2 doesn’t[p] 1 swerves 1,1 0,5[1-p] 1 doesn’t 5,0 -10,-10The Pure Strategy Nash Equilibrium for this game of “Chicken” are as follows: 5,0 (1 doesn’t, 2 swerves) 0,5 (1 swerves, 2 doesn’t).For Mixed Strategy:U1(1 swerves) = U1(1 doesn’t)1(q) + 0(1-q) = 5(q) -10 (1-q) 1q = 5q – 10 + 10q 1q = 15q – 10 -15q -15q ______________ -14q = -10 - - -14 -14___________ q = 5/7; (1-q) = 2/7U2(2 swerves) = U2(2 doesn’t)1(p) + 0(1-p) = 5(p) – 10(1-p) 1p = 5p – 10 + 10p 1p = 15p – 10 -15p -15p ______________ -14p = -10 - - -14 -14__________ p = 5/7; (1-p) = 2/7So the Mixed Strategy Nash Equilibrium is as follows:[(5/7 1 swerves + 2/7 1 doesn’t), (5/7 2 swerves + 2/7 2 doesn’t)]or (1 swerves with a probability of 5/7 and doesn’t with a probability of 2/7, 2 swerves with aprobability of 5/7 and doesn’t with a probability of 2/7).7.3Cole [q] [1-q] 2 arrives early 2 arrives late[p] 1 arrives early 1,1 -5,-1[1-p] 1 arrives late -1,0 3,3The Pure Strategy Nash Equilibria for this “Early-Late” game are as follows: 1,1 (1arrives late, 2 arrives late) 3,3 (1 arrives late, 2 arrives late).For Mixed Strategy:U1(1 arrives early) = U1(1 arrives late)1(q) – 5(1-q) = -1(q) + 3(1-q) 1q – 5 + 5q = -1q + 3 – 3q 6q – 5 = -4q + 3 +4q +5 = +4q + 5 ______________ 10 q = 8 - - 10 10 ________q = 4/5; (1-q) = 1/5U2(2 arrives early) = U2(2 arrives late)1(p) + 0(1-p) = 1(p) + 3(1-p) 1p = 1p + 3 – 3p 1p = -2p +3 +2p +2p __________ 3p = 3 - - 3 3 ______ p = 1; (1-p) = 0So the Mixed Strategy Nash Equilibrium is as follows:[(1 2 arrives early + 0 2 arrives late),(4/5 1 arrives early, 1/5 1 arrives late)]or (1 arrives early with the probability of 4/5 and late with a probability of 1/5; 2 arrives early withthe probability of 1 and late with a probability of 0).8. Admirer goes to library Admirer goes to coffee shopYou go to library 0,3 4,0You go to coffee shop 6,0 0,1a) There are no Pure Strategy Nash Equilibria in this game.4Cole For Mixed Strategy: U1(You go to library) = U1(You go to coffeeshop)0(q) + 4(1-q) = 6(q) + 0(1-q)4 – 4q = 6q +4q +4q___________ 4 = 10q- - 10 10q = 2/5; (q-1) = 3/5U2(Admirer goes to library) = U2(Admirer goes to coffeeshop)3(p) + 0(1-p) = 0(p) + 1(1-p) 3p = 1 – p +p +p _________ 4p = 1 - - 4 4p = ¼; (p-1) = ¾ So the Mixed Strategy Nash Equilibrium is as follows:[(1/4 You go to library + ¾ You go to coffeeshop), (2/5 Admirergoes to library + 3/5 Admirer goes to coffeeshop)].or(1 goes to library with a probability of ¼ and to the coffeeshop with a probability of ¾, 2 goes to library with a probability of 2/5 and goesto the coffeeshop with a probability of 3/5).b) Admirer goes to library Admirer goes to coffee shopYou go to library 4,3 0,0You go to coffee shop 0,0 6,1The Pure Strategy Equilibria in this game are as follows:4,3 (You go to library, Admirer goes to library) 6,1 (You go to coffee shop, Admirer goes to coffee shop)For Mixed Strategy:U1(You go to library) = U1(You go to coffeeshop)4(q) + 0(1-q) = 0(q) + 6(1-q) 4q = 6 – 6q +6q +6q ___________ 10q = 6 - - 10 10q = 3/5; (q-1) = 2/5U2(Admirer goes to library) = U2(Admirer goes to coffeeshop)5Cole 3(p) + 0(1-p) = 0(p) + 1(1-p) 3p = 1-p +p +p _______ 4p = 1 - - 4 4p = ¼; (1-p) = ¾So the Mixed Strategy Nash Equilibrium is as follows:[(1/4 (You go to library) + ¾ (You go to coffeeshop), 3/5 (Admirer goesto library + 2/5 (Admirer goes to coffeeshop)or(1 goes to library with the probability of ¼, coffeeshop with 3/4, 2 goes tolibrary with 3/5 probability, coffeeshop with 2/5 probability).9. 2a 2b 2c1a 0,9 3,0 1,51b1,2 5,4 4,31c 0,6 2,1 6,7a) The Pure Strategy Nash Equilibria for this game are as follows:5,4 (1b,2b)6,7 (1c,2c)b) 2a 2b 2c1a 0,9 3,0 1,51b1,2 5,4 4,31c 0,6 2,1 6,71b strongly dominates 1a.2c strongly dominates 2a.There are no more strongly nor weakly dominating strategies in this game.c) [q] [1-q] 2b 2c[p] 1b 5,4 4,3[1-p] 1c 2,1 6,7If P1 plays 1b then it is labeled probably p and 1c is then labeled with probability 1-p. Similarly,if P2 plays 2b then it is labeled with


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