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\begin{document}

\Course{ECO 100 Y}{Game Theory}
\Instructor{Martin J. Osborne}
\TestName{TERM TEST 1}
\Date{February 2000}
\Time{75 minutes}
\Aids{No aids allowed}
\QToBeAnswered{Answer all questions.}
\SpInstructions{{\bfseries To obtain credit, you must give arguments to
support your answers.}}

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\begin{enumerate}
\item \begin{enumerate}
\item (30) {Show that every finite strategic game has a mixed strategy Nash
equilibrium.}
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\solution{%
Use a fixed point theorem \ldots.
}

\pad

\item (10) {Give an example to show that not every finite strategic game has a
pure strategy Nash equilibrium.}

\solution{%
Matching Pennies.
}

\pad

\end{enumerate}

\nextpage

\item (40) {State precisely and prove a result relating the iterated
elimination of strictly dominated actions and rationalizable actions
profiles.}

\solution{%
   If a set of action profiles survives iterated elimination of strictly
dominated actions in a finite strategic game, \ldots
}

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\item \begin{enumerate}
\item \begin{enumerate}
\item (10) {Show that every trembling hand perfect equilibrium of an extensive
game induces a sequential equilibrium.}

\solution{%
Let \(\sigma \) be a trembling hand perfect equilibrium of an extensive game.
\ldots.
}
\pad
\item (5) {Give an example of a sequential equilibrium that is not associated
with any trembling hand perfect equilibrium.}

\solution{%
Here is an example \ldots.
}
\pad

\end{enumerate}

\item (5) {Given an example of an extensive game in which the set of trembling
hand perfect equilibria is disjoint from the set of behavioral strategy
profiles associated with the trembling hand perfect equilibria of its
strategic form.}

\solution{%
Here is an example \ldots.
}

\pad

\end{enumerate}



\end{enumerate}

\end{document}
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