Consider the following two symmetric games I S1 S2 S1-24 S2 0 1 II S1 S2 and S1 2…

Consider the following two symmetric games I S1 S2 S1-24 S2 0 1 II S1 S2 and S1 2…

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Consider the following two symmetric games I S1 S2 S1-24 S2 0 1 II S1 S2 and S1 2…
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Consider the following two symmetric games
I S1 S2
S1-24
S2 0 1
II S1 S2
and S1 2 0
$20 1
the former and latter matrices are numbered as I and II, respectively.
1. (25 points) Find all Pure strategy Nash equilibria of both games. Discuss Pareto optimality
of these equilibria if relevant.
2. (25 points) Find all mixed strategy Nash equilibria of both games and explain what is the
meaning of having a mixed strategy Nash Equilibrium.
3. (25 points) Write down the replicator equations describing the time variation of the frequency
of players adapating $1.
4. (25 points) What can you say about the stability of mixed strategy Nash equilibria of two
games given above under the replicator dynamics? Are they both stable unstable or just one
is stable? Why?

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