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In Problems 1-8, is the matrix game strictly determined?
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- 2. Give an example of a 2-player, zero-sum game with the following properties (by giving its payoff matrix from the perspective of the row player): • The row player has strategy set {1, 2} and the column player has strategy set {C1, C2} • The security levels of r₁, r2, C1, and c₂ are respectively −1, −2, 4, and 3.arrow_forwardQ5) Using graphical method to solve the following matrix game B1 B2 B3 A1 1 3 12 A2 8 6 2arrow_forwardd) Solve the following game for optimum strategies and the value of the game given the following matrix; Player A 18 6 11 7 Player B 4 6 4 2 13 7 5 17 3 6 12 2arrow_forward
- b) Consider the following game matrix: -10 -2 -1 7 -5 20 -10-10 7 -1 2 7 -10 7 -1 -10 Determine optimal mixed strategies to each player and give the value of the game. -1 7 -20 -10 -1 2-10 7 -5 20 -1 -1arrow_forwardIs this matrix game strictly dtermined for the following matrix? -10 -7 10 -7 Yes or Noarrow_forwardx and value of the original matrix game. In fractions please.....arrow_forward
- (ii) Explain Nonzero-sum game along with an example. For what value of A, the game with following payoff matrix is strictly determinable? B₂ A₁ A₂ A3 В1 λ -1 -2 6 λ 4 B3 2 -7 λarrow_forwardSolve the matrix game M, indicating the optimal strategies P and Q for row player R and column player C, respectively, and the value v of the game. (First determine if the game is strictly or nonstrictly determined.) M= P* = -3 2 3 -2 (Type an integer or simplified fraction for each matrix element.) Carrow_forward9. Solve the matrix game M, indicating the optimal strategies P*and Q*for row player R and column player C, respectively, and the value v of the game. (First determine if the game is strictly or nonstrictly determined. P*=________ (Type an integer or simplified fraction for each matrix element.) Q*= _____________ (Type an integer or simplified fraction for each matrix element.) v=arrow_forward
- Find the equilibrium pairs and values for the following game matrices. 6. 2 1 (Ь) -4 -1 4 4 11arrow_forwardProblem 2. Write down the linear program that solves the mixed security policies for the following matrix game. [3 1 0 1 2 2 4 1 1 3 5 5 0 0 0 6 A ||arrow_forwardProblem 3: (3+3+4 = 10 points) Let's look at a 2-player game where the players are A and B, and their actions are X, Y, and Z, with the following payoff matrix: B: X B: Y B: Z A: X 20,10 10, 20 1,1 A: Y 10, 20 20,10 1,1 A: Z 1,1 1,1 0,0 1) Reduce the payoff matrix using the Iterated Elimination of Strictly Dominated Strategies (IESDS) technique. 2) Do pure strategy Nash equilibrium/equilibria exist? If yes, what is/are the strategy/strategies for both players? (Hint: you should work on the reduced matrix from the previous subquestion). 3) Find the mixed strategy Nash equilibrium and both players' expected payoff at the equilibrium (Hint: you should work on the reduced matrix from the previous subquestion).arrow_forward
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