Two players battle in a game where the rules change between three modes.

In many competitions, two sides have opposite goals: whatever one player wins, the other loses. This is called a zero-sum game. Real-world systems can also jump between different states or environments. These changes are called regime switches. The authors studied a two-player, zero-sum game where the environment switches between three distinct regimes. To solve it, they used an advanced mathematical tool called viscosity solutions to study the core equations behind the game. They looked at how shifting among the three regimes alters the total game outcome, known as the value function. Their framework provides a clear method to find each player's best moves. Finally, when the switching regions have a known structure, they showed how to solve the value functions explicitly.

Why it matters

This matters because many real-world systems switch between different states, like markets or ecosystems. It gives tools to make optimal choices when competing in such changing conditions.

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