infinite game

The term "infinite game" is used in game theory to describe games that are not finite. Finite games have a limited number of options for each player, a finite number of players, and cannot continue indefinitely. Infinite games, in contrast, are more complex and can involve an endless sequence of moves or an unlimited number of possibilities.12

The concept of infinity itself, represented by the symbol ∞, refers to something without limits or bounds. In mathematics, infinity appears in various contexts, such as the number of points on a line or the endless sequence of counting numbers. The study of infinity has a long history, with ancient Greek philosophers grappling with its implications, and later mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz developing calculus to handle concepts of infinitely small numbers. Modern mathematics, particularly through the work of Georg Cantor, has explored different sizes of infinity, known as transfinite cardinals.32

While game theory primarily analyzes situations with interdependent decision-making, the concept of an "infinite game" highlights scenarios where the game's structure allows for unending play or an unlimited scope of actions.14