Table 1 This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). Find all Nash equilibria in this game. A Up Middle Down Left (1,4) (2, 2) (3, 1) B Center (6,5) (4, 6) (5,2) Right (3, 1) (5,5) (4,1)
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- し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?1. Consider the following normal-form game: Player 2 Left Right 30,20 10,10 10,30 20,20 Player 1 How many pure-strategy Nash Equilibria are there in this game? (a) 0 (b) 1 Up Down (c) 2 (d) 3 (e) 4 (f) None of the above Answer: 1b. The only Nash Equilirbium is (Up,Left).1. Repeated Game Consider the following normal form game. D Player 1 E F A 10, 10 -12,-1 15, -1 Player 2 B -1, -12 8,8 -1,-1 C -1, 15 -1,-1 0,0 (a) Suppose this game is played once. Find all pure strategy Nash equilibria. (b) Now suppose the game is played two times without discounting. Find all strategy profile that can be played in the first period in a SPNE. (c) Now suppose the game is played T times without discounting, where T is a finite number. Find the smallest T such that (E,A) is played in the first period. (d) Now suppose the game is played infinitely many times and the players have a same discount factor 8 < 1. Find the smallest d that can support the SPNE in which (D,A) is played in every period along the equilibrium path. (Hint: Players use the Grim-Trigger Strategy where (F,C) is used as a punishment).
- 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.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?Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?
- Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…NE 2). Consider the following extensive form game between two players. (1,10) u D 1 B X (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)5,3 4,4 3,6 7,6 Find the pure strategy nash equilibria
- Question 9 Player 1 Y Player 2 3,2 2 -0,1 1,3 -0,1 Which of the following is the Subgame Perfect Nash Equilbrium in this game?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 2.2Q2 Hand written plz Find any Nash equilibria in the following normal form game and indicate which Nash equilibria, if any, are strict. Player 2 b a W 3,5 1, -3 Player 1 x 2,-4 1,2 5,2 1, 1 7,1 5,2 Y 2 d C 2,5 -1,4 3,4 0,3 -2,5 3,2 0,2 3,2