KP 25 Find the value of the zero sum game given by the following payoff matrix

# Kp 25 find the value of the zero sum game given by

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Problem 8 (KP 2.5)Find the value of the zero-sum game given by the following payoff matrix and determine all optimal strategies for bothplayers:300322 Problem 9 (KP 2.11)Consider the following two-person zero-sum game. Both players simultaneously call out one of the numbers{2,3}. PlayerI wins if the sum of the numbers called is odd and player II wins if their sum is even. The loser pays the winner the productof the two numbers called (in dollars).Find the payoff matrix, the value of the game, and an optimal strategy for eachplayer. Problem 10 (KP 2.12)Consider the four-mile stretch of road shown in Figure 2.7 (in KP). There are three locations at which restaurants canbe opened: Left, Central, and Right. Company I opens a restaurant at one of these locations and company II opens tworestaurants (both restaurants can be at the same location). A customer is located at a uniformly random location along thefour-mile stretch. He walks to the closest location at which there is a restaurant and then into one of the restaurants there,chosen uniformly at random. The payoff to company I is the probability that the customer visits a company I restaurant.Determine the value of the game, and find some optimal mixed strategies for the companies.