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\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{all}
\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 Kakutani's fixed point theorem.}

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

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\end{enumerate}

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

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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.}
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\item (5) {Give an example of a sequential equilibrium that is not associated
with any trembling hand perfect equilibrium.}
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\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.}
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\end{enumerate}



\end{enumerate}

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