$($Table$)$ Based on the game theory table for Barbara and Helen $($with Barbara's profits in regular text and Helen's profits in italics$),$ a clear dominant strategy is that

$\backslash$table$[[\backslash$table$[[$Barbara$\text{'}$s$],[$Barbershop$]],,$Helen's Haircuts$],[,$Low Price,High Price$],[$Low Price,$$2\mathrm{.}000$ $$2,500,$$$3\mathrm{.}500,$$$1,000],[$High Price,$5600$ $$5,900,$$$2\mathrm{.}500,82,700]]$

Helen's best move is to charge a low price regardless of what Barbara does.

Helen's best move is to charge a high price regardless of what Barbara does.

both Helen and Barbara have a dominant strategy to charge a high price.

Barbara's best move is to charge a high price when Helen charges a low price.