I. (Mixed Strategy Nash Equilibrium.) Dorothy and Henry are playing one-stage game shown in the table below. Dorothy has three possible choices (Left, Middle, and Right), as does Henry (Up, Middle, and Down). pleas do not dist . Please do n Dorothy Left Middle Right Pleas entia t distribu listribute. Up (A, B) (6, 2) (3, 1) Henry Middle (2, 4) (8, 7) (5 5) Confidential. Please do lot distribute Down (1, 2) (4, 1) (C, D) dential. Please do n atril ot dist Find all of the Nash equilibrium (equilibria) in pure strategies and mixed strategies se do if idential. Pleas (a) A = 1, B = 1, C=7, and D = 4. (b) A =3, B = 1, C=4, and D = 0 fidential 2. (Sequential Game.) Parents have long used the rule "One divides, the other chooses" Con as a method of dividing desserts without a fight erupting. Suppose Bart and Lisa are brother and sister. Bart gets to cut a cake into 2 pieces. He can either cut a big and small piece, or he can cut two equal pieces. Lisa gets to choose which piece she would like. Suppose the pieces are put in front of Lisa and she picks either right or left. distribute. (a) Write out a game tree with Bart moving first. Suppose a big piece is worth 90 utils and a small piece is worth 10. Equal pieces are worth 50 each. Use backward induction method to find out the subgame perfect Nash equilib lease do not dist/ rium. (c) If the utility over cake for any given size piece is twice as big for Bart, does his denial. Pleas incentive to cut the cake change? distributefident dist r 3. (Stackelberg's Model of Oligopoly.) The market demand curve in a commodity chemical industry is given by Q = 600 - 3P, where Q is the quantity demanded Confides per month and P is the market price in dollars. Firm in this industry supply quantities every month, and the resulting market price occurs at the point at which the quantity demanded equals the total quantity supplied. Suppose there are two firms in this industry, Firm 1 and Firm 2. Each firm has an identical constant marginal cost of $80 per unit. distribute do L. Sun Confidential. Please to not distribute. itial. Plea ECON 3P21 distribute. Brock University Problem Set 9, Fall 2022-23 fide Department of Economics Co Please do (a) Find the Cournot equilibrium quantities for each firm. What is the Cournot equilibrium market price?co distribute. (b) Assuming that Firm 1 is the Stackelberg leader, find the Stackelberg equilib rium quantities for each firm. What is the Stackelberg equilibrium price? (c) Calculate and compare the profit of each firm under the Cournot and Stackel- case do not dis berg equilibria. Under which equilibrium is overall industry profit greater