Answer $3.$A to $3.$F based on the following information about two firms are planning to market network systems for Office Information Management. Each firm can develop either a fast, high$-$quality system $($H$),$ or a slower, low$-$quality system $($L$).$ Market research indicates that the resulting profits to each firm for the alternative strategies. The estimated profit figures over the product life are summarized in the following game payoff matrix. In each cell, the first payoff is the profit of firm $1$ and the second one is the profit of firm $2.$ The profit figures are given in million US$$.$

Firm $2$

Firm $1$

$\backslash$table$[[,$H$,$L$],[H,300,260,240,280],[$L$,260,220,280,240]]$

$3.$A$.$ Does any of the firms have a strictly dominant strategy? Justify your answer.

$[2]$

$3.$B$.$ Find the Nash equilibrium of the game. Justify your answer.

$3.$C$.$ Is the Nash equilibrium Pareto optimal? Why or why not?

$[2]$

$3.$D$.$ Draw the game tree if Firm $1$ moves first.

$[2]$

$3.$E$.$ If Firm $1$ gets to decide before Firm $2$ and develops its system before Firm $2,$ will it develop a high quality system? Why?

$[2]$

$3.$F$.$ Is there a first mover's advantage?

$[2]$