Attempts $1\mathrm{.}7$ Keep the Highest $1\mathrm{.}7/3$

$5.$ Problems and Applications Q$5$

Synergy and Dynaco are the only two firms in a specific high$-$tech industry. They face the following payoff matrix as they decide upon the size of their research budget:

$\backslash$table$[[$Dynaco$\text{'}$s Decision,,Synergy's Decision$],[,$Large Budget,Small Budget$],[$Large Budget,$$30$ million, $$20$ million,$$70$ million, $$0],[$Small Budget,$$0,$ $$30$ million,$$50$ million, $$40$ million$]]$

If Synergy believes Dynaco will go with a large budget, it will choose a large grad budget. If Synergy believes Dynaco will go with a small budget, it will choose a $q,$ budget. Therefore, Synergy $$ a dominant strategy.

If Dynaco believes Synergy will go with a large budget, it will choose a $q,$ budget. If Dynaco believes Synergy will go with a small budget, it will choose a $q,$ budget. Therefore, Dynaco $$ a dominant strategy.

True or False: There is a Nash equilibrium for this scenario. $($Hint: Look closely at the definition of Nash equilibrium.$)$

True

False