Solve the Games with the Given Payoff Matrix $$P = \left[ \begin{array} { c c c } - 1 & 1 & 2 \\2 & - 1 & - 2 \\1 & 2 & - 1\end{array} \right]$$

question 4

Multiple Choice

Solve the games with the given payoff matrix. $$P = \left[ \begin{array} { c c c } - 1 & 1 & 2 \\2 & - 1 & - 2 \\1 & 2 & - 1\end{array} \right]$$

• A) \(C = \left[ \begin{array} { l }
• \frac { 5 } { 9 } \\
• \frac { 2 } { 9 } \\
• \frac { 2 } { 9 }
• \end{array} \right]\) , \(R = \left[ \begin{array} { l l l }
• \frac { 7 } { 18 } & \frac { 1 } { 18 } & \frac { 5 } { 9 }
• \end{array} \right]\) , \(e = - \frac { 85 } { 18 }\)
• B) \(C = \left[ \begin{array} { l }
• \frac { 5 } { 9 } \\
• \frac { 2 } { 9 } \\
• \frac { 2 } { 9 }
• \end{array} \right]\) , \(R = \left[ \begin{array} { l l l }
• \frac { 7 } { 18 } & \frac { 1 } { 18 } & \frac { 5 } { 9 }
• \end{array} \right]\) , \(e = - \frac { 31 } { 18 }\)
• C) \(C = \left[ \begin{array} { c }
• \frac { 5 } { 9 } \\
• \frac { 7 } { 18 } \\
• \frac { 1 } { 18 }
• \end{array} \right]\) , \(R = \left[ \begin{array} { l l l }
• \frac { 5 } { 9 } & \frac { 1 } { 18 } & \frac { 7 } { 18 }
• \end{array} \right]\) , \(e = \frac { 5 } { 18 }\)
• D) \(C = \left[ \begin{array} { c }
• \frac { 1 } { 18 } \\
• \frac { 7 } { 18 } \\
• \frac { 5 } { 9 }
• \end{array} \right]\) , \(R = \left[ \begin{array} { l l l }
• \frac { 5 } { 9 } & \frac { 1 } { 18 } & \frac { 7 } { 18 }
• \end{array} \right]\) , \(e = - \frac { 85 } { 18 }\)
• E) \(C = \left[ \begin{array} { c }
• \frac { 5 } { 18 } \\
• \frac { 5 } { 18 } \\
• \frac { 4 } { 9 }
• \end{array} \right]\) , \(R = \left[ \begin{array} { l l l }
• \frac { 5 } { 9 } & \frac { 1 } { 18 } & \frac { 7 } { 18 }
• \end{array} \right]\) , \(e = - \frac { 31 } { 18 }\)

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Definitions:

Innate Behaviors

Behaviors that are genetically coded and present at birth, not learned through experience, such as reflex actions in infants.

Inherited Response

A reaction or behavior that is genetically passed down from one generation to the next, often instinctual in nature.

Sucking Response

An innate reflex in infants, triggering them to instinctively suck anything that touches the roof of their mouth.

Philosophy Of Dualism

The belief that reality or existence is divided into two distinct and irreducible elements, often referring to the division of mind and body or material and immaterial.