In the game paper, scissors, rock there are two players: player I and player II. Each...

 

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In the game "paper, scissors, rock" there are two players: player I and player II. Each player chooses one of the three objects: paper, scissors, or rock. The payoff to player I is given by the following table: paper scissors rock paper scissors rock -1 0 1 1 -1 1 -1 0 As we will learn later in this course, there is an important number V called the value of the game. To compute the value of the game "paper, scissors, rock" we will use the formula V = min max(93-92, 91-93, 92-91}. 91 +92 +93 1 9.92-9320 That is, V is the optimal value of the following piecewise linear convex optimization problem: minimize subject to f(91,92,93) +92 +93=1 91-92, 9320 where f(1.92.93)= max(93-92, 91-93-92-91). (a) Convert this piecewise linear convex optimization problem into a LPP by introducing a new variable 2. (b) Find the optimal value of the LPP in part (a). (c) Find the optimal solution to the LPP in part (a). Hint: from part (b) you know the value of the optimal solution. Note: in parts (b) and (c) you do not need to follow any particular method. You can just guess the solution and then prove that your guess is correct. In the game "paper, scissors, rock" there are two players: player I and player II. Each player chooses one of the three objects: paper, scissors, or rock. The payoff to player I is given by the following table: paper scissors rock paper scissors rock -1 0 1 1 -1 1 -1 0 As we will learn later in this course, there is an important number V called the value of the game. To compute the value of the game "paper, scissors, rock" we will use the formula V = min max(93-92, 91-93, 92-91}. 91 +92 +93 1 9.92-9320 That is, V is the optimal value of the following piecewise linear convex optimization problem: minimize subject to f(91,92,93) +92 +93=1 91-92, 9320 where f(1.92.93)= max(93-92, 91-93-92-91). (a) Convert this piecewise linear convex optimization problem into a LPP by introducing a new variable 2. (b) Find the optimal value of the LPP in part (a). (c) Find the optimal solution to the LPP in part (a). Hint: from part (b) you know the value of the optimal solution. Note: in parts (b) and (c) you do not need to follow any particular method. You can just guess the solution and then prove that your guess is correct.