Solve the Problem $2 \times 5$ Matrix Game Can Be Found as Follows: Obtain 5 Linear

question 41

Multiple Choice

Solve the problem.
-The optimal strategy for a $2 \times 5$ matrix game can be found as follows: obtain 5 linear functions by finding the inner product of $x ( t ) = \left[ \begin{array} { c } 1 - t \\ t \end{array} \right]$ with each of the columns of the payoff matrix A. Graph the 5 linear functions on a t-z coordinate system. Then $v ( x ( t ) )$ is the minimum value of the 5 linear functions which will be seen on the graph as a polygonal path. The z-coordinate of any point on this path is the minimum of the corresponding $z$ coordinates of points on the 5 lines. The highest point on the path $v ( x ( t ) )$ is M. Suppose that only the lines corresponding to columns 1 and 4 of matrix $A$ pass through the point $\mathrm { M }$ . What can be said about the optimal column strategy $\hat { y }$ ?

• A) \(\hat { y } = \left[ \begin{array} { l } \frac { 1 } { 2 } \\ 0 \\ 0 \\ \frac { 1 } { 2 } \\ 0 \end{array} \right]\)
• B) \(\hat { y } = \left[ \begin{array} { l } 0 \\ c _ { 2 } \\ c _ { 3 } \\ 0 \\ c _ { 5 } \end{array} \right]\) where \(c _ { 2 } + c _ { 3 } + c _ { 5 } = 1\)
• C) \(\hat { \mathrm { y } } = \left[ \begin{array} { l } \mathrm { c } _ { 1 } \\ 0 \\ 0 \\ \mathrm { c } _ { 4 } \\ 0 \end{array} \right]\)
• D) \(\hat { y } = \left[ \begin{array} { l } 0 \\ 0 \\ 0 \\ 1 \\ 0 \end{array} \right]\)

Acknowledge the evolutionary similarities and differences in brain structures across species.

Distinguish between the roles of various brain structures in sensory processing, memory formation, and vital functions.

Grasp the concept of representation and organization in the cerebral cortex in relation to body control and sensory processing.

Identify the primary components of the limbic system and their roles in emotional and endocrine regulation.

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Definitions:

Mature Neurons

Fully developed nerve cells that have reached their final differentiated form, participating actively in the brain and nervous system's functions.

Resilient

The capacity of an individual to quickly recover from difficulties or to adapt successfully to stress and adversity.

Neural Circuits

Networks of neurons interconnected by synapses, responsible for processing and transmitting information through electrical and chemical signals.

Repressed Memories

Memories that have been unconsciously blocked due to being associated with a high level of stress or trauma.