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In Problems 1 and 2, 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_forward2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.arrow_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
- Create a 3x3 payoff matrix for a two person zero sum game (cannot be scissors, paper, rock)arrow_forwardFind the equilibrium pairs and values for the following game matrices. 6. 2 1 (Ь) -4 -1 4 4 11arrow_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
- 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_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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