* 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.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 3T
Related questions
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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