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