Repeated games - exercises¶

1. Define a repeated game.
2. Define a strategy for a repeated game.
3. Write the full potential history $\bigcup_{t=0}^{T-1}H(t)$ for repeated games with $T$ periods in the following cases:
1. $S_1=S_2=\{0, 1\}$ and $T=2$
2. $S_1=\{r_1, r_2\}\;S_2=\{c_1, c_2\}$ and $T=3$
4. Obtain a formula for $\left|\bigcup_{t=0}^{T-1}H(t)\right|$ in terms of $S_1, S_2$ and $T$.
5. State and prove the theorem of sequence of stage Nash equilibria.
6. Obtain all sequence of stage Nash equilibria as well as another Nash equilibrium for the following repeated games:
1. $A = \begin{pmatrix} 3 & -1\\ 2 & 4\\ 3 & 1 \end{pmatrix} \qquad B = \begin{pmatrix} 13 & -1\\ 6 & 2\\ 3 & 1 \end{pmatrix} \qquad T=2$
2. $A = \begin{pmatrix} 2 & -1 & 8\\ 4 & 2 & 9 \end{pmatrix} \qquad B = \begin{pmatrix} 13 & 14 & -1\\ 6 & 2 & 6 \end{pmatrix} \qquad T=2$
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