Two companies, Company A and Company B, are deciding whether each should implement a new pricing strategy, which may or may not result in a price war.

If both companies reduce (discount) their current prices, each company will end up with $175K in revenues for the month.

If neither company discounts its current prices, each company will end up with $400K in revenues for the month.

If Company A discounts its prices and Company B does not, Company A will end up with $650K of revenues for the month and Company B will end up with $450K in revenues for the month.

If Company B discounts its prices and Company A does not, Company B will end up with $325K in revenues for the month, and Company A will end up with $450K in revenues for the month.

Depict this game three ways.

First, as a simultaneous game in a game box. Solve the game by identifying any and all Nash Equilibrium.

Next, as a two-stage game using a game tree with Company A going first. Solve this game and identify the Nash Equilibrium.
Next, as a two-stage game using a game tree with Company B going first. Solve this game and identify the Nash Equilibrium.
Does either Company have a first-mover advantage? If so, which company?