b A -10, 30 B 6,-1 0,0 C -1,20 -20, 100 What is the Nash Equilibrium of this game? a 500,0 O a. (C, c) O b. (C, b) O c. (A, a) O d. (B, b) C 20, 12 8, -2 7,800
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- rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.Question Completion Status: II -10 -20 3. -30 -10 2. -20 3 -30 Write a normal form for this game. How many pure-strategy Nash Equilbria are there in this game? OA1 OB.2 OC3 OD.4 OES OF. More than 5FOOP 6. (a) For the following extensive-form game: i. Identify the pure and mixed strategy Nash Equilibria. ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in part (a)? Explain (a couple of sentences should suffice). (3,1) A D B C (-2,-2) (2,5) D (0,7)
- li5,3,2) A (0,1, 1) -(3,2,6) (0.6,5) Y(2,1,4) R /6,3,0) -40,6) -(3,1,7) Is there Subgame Perlact Nash Equilibaion! I se what s it? 30,24. Two individuals play the following infinitely repeated prisoner's dilemma game: Player A Cooperate Defect Player B Cooperate 3,5 7,0 Defect 0,6 1, 1 Assume that both players discount future payoffs at rate 8<1. (a) If both players play 'cooperate' every period, then what are their total payoffs?MC Qu. 07-42 (Algo) Suppose Firm A and Firm... Suppose Firm A and Firm B are considering whether to invest in a new production technology. For each firm, the payoff to investing (given in thousands of dollars per day) depends upon whether the other firm invests, as shown in the accompanying payoff matrix. Firm A Don't Invest Invest Multiple Choice O What is the Nash equilibrium of this game? O Invest 9 for A 6 for B 7 for A 3 for B Firm B Firm A invests, and Firm B doesn't invest. Firm A invests, and Firm B invests. Not Invest 5 for A 7 for B Firm A doesn't invest, and Firm B invests. 12 for A 8 for B Firm A doesn't invest, and Firm B doesn't invest.
- Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?3. 1 2 J K 2 1 2 0 0 K 3 3 E/ 1.1 2.2 B G 2 -2 a.) How many Subgames does this Game have? b.) Convert this Game Tree into matrix form. c.) Find all Pure Strategy Nash Equilibria of this Game. d.) Find all Subgame Perfect Nash Equilibria of this Game. (Pure and Mixed) 2 2.2Problem 2. (SPNE 2). Consider the following extensive form game between two players. (1,10) .. D 2 1 B X Y (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)
- 2. Consider the static game represented by the following payoff matrix: r с 1,1 2, -1 -1,2 R 0,0 (a) Find the Nash equilibrium of the above game. (b) If above static game is repeated TCostco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3BConsider the following extensive-form game. U D A B A B -6,6 X Y X Y P 3,8 -8, 1 1,2 -2, 1 5,5 -0,0 The dashed lines represent information sets. (a) Represent this game in normal-form. (b) Derive the Nash equilibria in pure strategies. (c) Describe the (proper) subgames of this game. (d) Derive the subgame perfect Nash equilibria in pure strategies.SEE MORE QUESTIONS