Suppose that Pentax and Leica are the only camera makers that can invest in a new technology that would revolutionise the industry. The following matrix shows the payoffs $($in millions of euros$)$ from investing in this technology:

Leica

I Pentax Invest Do Not Invest

$\backslash$table$[[,$Invest,Do Not Invest$],[,,-80,,0],[$Do Not Invest,$-80,,560,0],[,,560,,],[,0,,,]]$

a$.$ If both firms move simultaneously, does either firm have a dominant strategy? Explain.

b$.$ What is the Nash equilibrium of both firms move simultaneously?

c$.$ The German governments commits to paying Leica a lump$-$sum subsidy of $100$ million euro if it invests in this technology. What is the Nash equilibrium?

d$.$ If Leica does not receive a subsidy but has a technical advantage over Pentax concerning this technology and has a head start $($i$.$e$.$ moves first$),$ what is the Nash equilibrium?