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- 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,Problem 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)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.
- AsapSolve this game using iterated elimination of strictly dominated strategies. Write down your process as well as your final solution. a b d e А 31,-1 | 1,3 |1,0 |32,-2 1,1 B 62,-3 -3,-2 27,-3-3,43 -4,17 с 53,-1 | -1,0 194,-33,-3 |-1,2 D0,-35 -3,37 -4,41 0,-14 -2,15 E -23,-2 -3,86 0,-15 -3,55 -4,7o1. 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).
- >A Moving to another question will save this response. uestion 8 It is possible for companies to use some combination of push and pull strategy. True False Moving to another question will save this response. 10 #3 00 3. 10 5 4) %24Y's possible prices $40 SES $40 $60 X's possible prices $69 $57 $50 a) Outcome under credible threat in one time game? b) Outcome when repeated game? B $35 $55 D $58 $59 $55Question Completion Status: Gekko QUESTION 8 Good Quality a Poor Quality SERDE 1 INSGE 19 2 Good Quality Wonka 10 Gekko = 10 Wonka = 12 Gekko = 9 1 Wonka Refer to Table 17-7. Wonka and Gekko agree to cooperate so as to maximize total profit. If this game is played repeatedly and Wonka uses a tit- strategy, it will choose a O a. good quality product in the first round and in subsequent rounds it will choose whatever Gekko chose in the previous round. O b. poor quality product in all rounds, regardless of the choice made by Gekko. C. good quality product in all rounds, regardless of the choice made by Gekko. d. poor quality product in the first round and in subsequent rounds it will choose whatever Gekko chose in the previous round. Poor Quality Wonka = 9 Gekko = 12 Click Save and Submit to save and submit. Click Save All Answers to save all answers. Wonka = 11 Gekko = 11 O Pleshow! www 0 R Aa
- Tech is playing State in the last conference game of theseason. Tech is trailing State 21 to 14 with 7 seconds left inthe game, when they score a touchdown. Still trailing 21 to20, Tech can either go for two points and win or go for onepoint to send the game into overtime. The conferencechampionship will be determined by the outcome of thisgame. If Tech wins they will go to the Sugar Bowl, with apayoff of $9.2 million; if they lose they will go to the GatorBowl, with a payoff of $1.5 million. If Tech goes for twopoints there is a .30% chance they will be successful andwin (and a .70% chance they will fail and lose). If they gofor one point there is a 0.98 probability of success and a tieand a 0.02 probability of failure. If they tie they will playovertime, in which Tech believes they have only a 20%chance of winning because of fatigue.a. Use decision-tree analysis to determine if Tech shouldgo for one point or two points.b. What would Tech’s probability of winning the game inovertime…a 12, 9, 3 m 1 N b 10, 9, 4 7" 11, 15, 1 B 10, 20, 10 What's the possible outcome of this game?3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 8760