In a Nash equilibrium, if one firm changes its strategy while others keep theirs unchanged, it is guaranteed that the changing firm will increase its payoffs.

In a Nash equilibrium, each player chooses their best strategy given the strategies of the others, meaning no one can benefit by changing their strategy alone. If one firm decides to change its strategy while the others stick to theirs, it does not guarantee that the changing firm will increase its payoffs. This is because the payoffs depend on the responses of the other firms, which may not favor the firm that changes its strategy. For example, if three firms are producing similar products and one firm lowers its price, it might attract some customers, but if the other firms also lower their prices in response, the changing firm may end up with no increase in profit. Thus, a firm can actually lose out by changing its strategy in a Nash equilibrium.