Consider the following two-person zero-sum game: 3-2 5-1 1 4 42 5 11 3 If the row player uses the mixed strategy (3,2,0), determine an optimal pure counter-strategy for the column player.
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- Solve the matrix game. -2 3 1 1 -1 -2 -3 -3 2 The optimal strategy for the row player is P*=______ (Type an integer or simplified fraction for each matrix element.) The optimal strategy for the column player is Q*=_______ (Type an integer or simplified fraction for each matrix element.) The value for the game is v=__________ (Type an integer or a simplified fraction.)QUESTION 9 D 2 C D D, D OD, C C, D C II C (2,2) (4,0) (0,4) (3,3) In the dynamic game represented by the graph above, the numbers inside paranthesis show the payoffs of Player 1 and Player 2, respectively. The Nash equilibrium of this game is for Player 1 to choose O C, C and Player 2 to chooseQuestion 1 Using your knowledge of the "method of elimination.of dominated strategy". solve for the equilibrium solution(s) to the following pay-off matrix for two players. Player A Player B Strategyl Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy1 (40, 200) Strategy 2 (60, 25) Strategy 3 (88, 55) (55,102) (45, 142) (109) 42) K09. 120) (50, 100) (99, 155)70 la. (80. 100) K104, 55) (44,90) (100,50) C403)165)(17 190 (60, 160) (155,115) (95.120) (50, 90) (84, 100) Strategy 4 Strätegy 5 172) 140) (85, 145) (48, 200) 123)125) (100, 145) Is your solution in "a above unique? Why? b. Present the following extended form of pay-off matrix in a normal form pay-off matrix for the player Extended Form of Pay-»ff Matrix Player B Strategy 1 (40, 20) (30,25) Strategy 2 (90, 300) (85.55) 30 25 Player A Strategy 1 Strategy 2 20
- 1. You (row)/Your Crush (column) McElroy Corcoran The Dining Hall Game McElroy 3,2 0,0 a) Represent this game in extensive form b) How many subgames does this game have? Corcoran 1,1 2,3Explain the concept of two-person zero- sum game and saddle point. Also provide a suitable example. Determine which of the following two-person zero-sum games are strictly determinable and fair. Give the optimum strategies for each player in the case of it being strictly determinable. Player A Player B B2 вз 4 B1 A1 5 -1 2 A2A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
- 11) In the following game, list any dominant or dominated strategies. Then, solve the game Player 2 Left Center Right Player 1 Up 1,2 4,6 5,5 Down 6,3 2,4 3,1(c) Consider the following two-player, zero-sum game: Y1 Y2 X1 -2 8 X2 10 -5 What is the outcome of this game?1. A row of minus signs is written on a whiteboard (can be any number). Two players take turns in replacing either a single minus sign by a plus sign or two adjacent minus signs by two plus signs. The player who makes the last move wins. Discuss the possible strategy for the first mover to force a win.
- Problem 1 Consider the following two-person game: 1 2 C ea Prsover's D U 4, 7 6,0 10, 4 11, 5 M 5, 4 7,5 0, 3 6, 3 D 3, 12 5, 10 12, 5 8, 16 Use successive elimination of dominated strategies to find the optimal strategies.Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.II. Determine which of the following two-person zero-sum games are strictly determinable and fair. Give the optimum strategies for each player in the case of it being strictly determinable. a- Player A Player B B1 B2 B3 A1 8 2 4 A2 5 -1 3 b. II II V V I -4 -2 -2 1 A II 1 -1 III -6 -5 -2 -4 4 IV 3 1 -6 0 -8 3.