In Problems 9-16, the matrix for a strictly determined game is given. Find the value of the game. Is the game fair?
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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_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_forwardSuppose that we further alter the game from question 2 as follows: now whenever both players select the same strategy, both receive a payoff of 2. Note that this is no longer a zero-sum game. (a) Give the payoff matrix for this game. As usual, you should list Rosemary's payoffs first and Colin's payoffs second in each cell. (b) Underline the best responses for each player to each of the other players' strate- gies in your payoff matrix. Then, find and give all Pure Nash equilibria for the modified game.arrow_forward
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