1. For each of the following payoff matrices of 2-person, simultaneous games,
(a)
$\begin{pmatrix} (1,3) & (4,6) \\ (2,4) & (1,2) \end{pmatrix}$
(b)
$\begin{pmatrix} (-1,2) & (3,4) & (1,-3) \\ (2,1) & (5,-1) & (3,3) \\ (4,2) & (-2,2) & (2,0) \end{pmatrix}$
(i) Circle all pure Nash equilibria.
(ii) For each pure Nash equilibrium, label it as PO (Pareto optimal) or NPO (non-
Pareto optimal).
2. For the following 2-person simultaneous game,
$\begin{array}{c|cc} & C1 & C2 \\ \hline R1 & (5,1) & (-4,0) \\ R2 & (2, 4) & (-2,7) \end{array}$
(a) Find all the pure Nash equilibrium(s) (if exist) and the corresponding payoffs.
Determine if each of them is Pareto optimal.
(b) Given that a non-pure Nash equilibrium exists, find it and the corresponding
payoffs.
(c) Find Row's prudential strategy and security level.
(d) Find Col's prudential strategy and security level.
