The second game (shown below) is a repeated game. It represents their behavior in twosuccessive periods. Within each period they act simultaneously, but recall what has happenedpreviously. In the second period, In the second period, the players acquire the same payoffsthey did in the first, while retaining the payoffs received in the first. The figure below showsonly two of the four possible subgames for the second period.Nash Equilibrium(NE)A:Period 1B:AA: 4A: 2B: 1B: 2Period 2Nash EquilibriumNash Equilibrium(NE)A:(NE)A:AAВ:B:A: 6A: 4A: 7A: 5A: 4A: 2A:5A: 3B: 6B: 7B: 4B: 5B: 7B: 8B:5B: 6a. Solve the game by the Rollback method. Identify the dominantstrategies and circle the Nash Equilibrium for each subgame andwrite it above its starting node.

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Answered: The second game (shown below) is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Instructions: Show all your work (including bi-matrix and/or game tree when relevant). 1. Two investors have each deposited 4 (all amounts are in $10,000s) with a bank. The bank has invested these deposits in a long-term project. If both investors make withdrawals at date 1 then each receives 2 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives 4, the other receives 0, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives 8 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 10, the other receives 6, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 8 to each investor and the game ends. Find the subgame-perfect outcomes.
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Solve the game with the given payoff matrix. P = -6 0 1 -9 0 0 0 -1 -2 a) Find the optimal row player strategy b) Find the optimal column player strategy c) Find the expected value of the game
Best Treats Introduce $2 Introduce Healthy Snacks Do not Introduce $9 $11 $9 $6 $0 Do not Introduce $3 50 $0 Healthy Snacks and Best Treats are two firms competing in the health food snacks market. Both are considering introducing a new health food snack made purely of dried power fruits. The payoff matrix shows their net economic profit in millions for the different strategies. Refer to the payoff matrix above. In reference to the Nash equilibrium/equilibria in this game, which of the following is true? Best Treats Introduce and Healthy Snacks Introduce is a Nash equilibrium. There are no Nash equilibria in this game. Best Treats Do Not Introduce and Healthy Snacks Do Not Introduce is a Nash equilibrium. Best Treats Introduce and Healthy Snacks Do Not Introduce is a Nash equilibrium.
Find the optimal strategies, P and Q, for the row and column players, respectively. -2 1-3 P= 5/13 Q= 5/13 Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) E= Which player does the game favor, if any? OR C Oneither
operations research 2
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Calculate the expected payoff of the game with payoff matrix 2 0-2 3 -1 0 0 -3 P = -2 0 1 3 1-1 2 using the mixed strategies supplied. HINT [See Example 1.] R = [0 0 0 1], C = [0 0 1 0]" %3D
Consider the following payoff matrix. -1 P = 0 -1 (a) Find the optimal mixed row strategy. I 1 (b) Find the optimal mixed column strategy. (c) Find the expected value of the game in the event that each player uses his or her optimal mixed strategy.
7.
1. Suppose we have a 2-player zero-sum game where the strategy set of the row player (resp. the column player) is R = {₁,..., rk} (resp. C = {C₁,..., ce}) and where the payoff matrix is A (ai). If (r₁, c₁) and (r2, C₂) are both Nash equilibria, show that they have the same payoff (i.e. a11 a22). [Do this directly using the definitions and without using any theorems from the lectures.] = =
The payoff matrix for a game is given by 2 -3 -3 Compute the expected payoffs of the game for the pairs of strategies in parts (a-d). (Round your answers to one decimal place.) (a) P= E-1 (b) P= %3D E = (c) P = E = [0.8 02).0-0] (d) P = E = Which of these pairs of strategles is most advantageous to R? O (a) O (b) O () O (d)

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