Answer
a) Synergy doesn't have a dominant strategy.
b) Dynaco has a dominant strategy of a large budget.
c) Yes, there is a Nash equilibrium for this scenario. Both firms will have large budgets.
Work Step by Step
a) If Dynaco was to have a large budget, Synergy would be better off with a large budget (gaining 20 million dollars) than with a small budget (gaining nothing). However, if Dynaco was to have a small budget, Synergy would be better off with a small budget (gaining 40 million dollars) than with a large budget (gaining 30 million dollars).
b) If Synergy was to have a large budget, Synergy would be better off with a large budget (gaining 30 million dollars) than with a small budget (gaining nothing). However, if Synergy was to have a small budget, Synergy would be better off with a large budget (gaining 70 million dollars) than with a large budget (gaining 50 million dollars).
c) Synergy doesn't have a dominant strategy. However, Dynaco has a dominant strategy of having a large budget. Thus, Synergy would be better off with a large budget than a small budget.