The maximin strategy in game theory is a decision-making approach used when players want to avoid the worst possible outcomes in uncertain situations. Instead of aiming for the highest potential gain, a player using the maximin strategy selects the option that guarantees the best result among the least favorable outcomes. This approach provides security, helping players manage risk when other players' choices are unknown.

Consider two software companies deciding whether to release a new version of their app with advanced features. If Company X releases the latest version, the minimum payoff might be a significant user loss. This outcome could arise if the unproven app's performance doesn't meet expectations, resulting in negative user reviews and decreased downloads. If Company X holds off on releasing the new version of its app, its minimum payoff is neutral since it keeps its existing user base steady. By choosing the maximin strategy, Company X would avoid releasing the new version since the worst outcome—losing users—is more significant if it is released.

Company Y faces a different situation. If it releases its latest update, the minimum payoff might be a slight increase in user engagement, even in a conservative scenario where only a few users adopt the new features. On the other hand, if Company Y delays the release, it risks losing users to competitors who offer similar features sooner, making its minimum payoff negative in that case. Applying the maximin strategy, Company Y would go ahead with the release, as the worst-case outcome still secures some engagement.

By minimizing the worst outcomes, the maximin strategy helps companies make decisions that prioritize stability and manage risk, particularly when facing competitive uncertainty.