* Consider the following parametric matrix game: -1 Р -3 C = where P is an arbitrary integer parameter. -2 -3 2+p 1. For each value of p, check whether the game has a solution in pure strategies, and if so, write out all such solutions. Write your arguments. 2. For p = 1, find the gain-floor vPS (C) and loss-ceiling vS (C) of C in pure strategies. Is it true that v(C) > 0, where v(C) denotes the value of the game in mixed strategies? Justify your answer using the value of US (C)¹. 3. Setting p = 0, solve the matrix game C by the dual simplex method in mixed strategies. This involves finding an optimal mixed strategy for Player I, an optimal mixed strategy for Player II, and the value of the game. Hint: If v(C) > 0 does not hold, add a sufficiently large positive constant to C to obtain a matrix game with a guaranteed positive value.
* Consider the following parametric matrix game: -1 Р -3 C = where P is an arbitrary integer parameter. -2 -3 2+p 1. For each value of p, check whether the game has a solution in pure strategies, and if so, write out all such solutions. Write your arguments. 2. For p = 1, find the gain-floor vPS (C) and loss-ceiling vS (C) of C in pure strategies. Is it true that v(C) > 0, where v(C) denotes the value of the game in mixed strategies? Justify your answer using the value of US (C)¹. 3. Setting p = 0, solve the matrix game C by the dual simplex method in mixed strategies. This involves finding an optimal mixed strategy for Player I, an optimal mixed strategy for Player II, and the value of the game. Hint: If v(C) > 0 does not hold, add a sufficiently large positive constant to C to obtain a matrix game with a guaranteed positive value.
Chapter7: Matrices And Determinants
Section7.1: Matrices And Systems Of Equations
Problem 1ECP: Determine the dimension of the matrix 14710238.
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Question
Transcribed Image Text:* Consider the following parametric matrix game:
-1 Р -3
C
=
where P is an arbitrary integer parameter.
-2 -3 2+p
1. For each value of p, check whether the game has a solution in pure strategies, and if so,
write out all such solutions. Write your arguments.
2. For p = 1, find the gain-floor vPS (C) and loss-ceiling vS (C) of C in pure strategies. Is
it true that v(C) > 0, where v(C) denotes the value of the game in mixed strategies?
Justify your answer using the value of US (C)¹.
3. Setting p = 0, solve the matrix game C by the dual simplex method in mixed strategies.
This involves finding an optimal mixed strategy for Player I, an optimal mixed strategy
for Player II, and the value of the game.
Hint: If v(C) > 0 does not hold, add a sufficiently large positive constant to C to obtain
a matrix game with a guaranteed positive value.
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