Hierarchical Games with Uncertain Outcomes Reshape Strategic Decision-Making
The article discusses a type of game where some players make decisions before others, called Nash-Stackelberg-Nash games. The researchers focus on these games when there are uncertainties that depend on the players' choices, which haven't been studied much before. They create a new way to define when the game reaches a balance point, combining two existing concepts. By using a mathematical theorem, they prove that a balance point always exists in these games with decision-dependent uncertainties. An example is given to show how these uncertainties can affect the game's outcome.