In a game where two firms compete on price, if both firms set their prices equal to the marginal cost and neither can improve their profits by unilaterally changing their prices, what is this situation called?

The situation you're describing is called a Nash Equilibrium. In this case, both firms have decided to set their prices at the marginal cost, which is the cost of producing one more unit of their product. At this point, neither firm can increase its profits by changing its price on its own because doing so would either lead to a loss or no gain in sales. For example, if Firm A raises its price while Firm B keeps its price at marginal cost, customers will likely buy from Firm B instead. Therefore, both firms remain at this price point because any change would not benefit them, creating a stable situation known as Nash Equilibrium.