Game theory is a branch of mathematics that studies decision making and strategic interactions between individuals or groups. It is used to analyze situations in which participants must make choices that affect the outcome of a game or situation. Game theory provides a framework for understanding how individuals or groups make decisions, taking into account the actions and reactions of others.
Since this game was first described nearly 60 years ago, there has been a dilemma within the game — a set of positions where it was thought that no game optimal solution existed. But now, Milutinovic and his colleagues have proved in a new paper published in the journalthat this long-standing dilemma does not actually exist and introduced a new method of analysis that proves there is always a deterministic solution to the wall pursuit game.
So Milutinovic and his coauthors came up with a new way to approach the problem, using a mathematical concept that was not in existence when the wall pursuit game was originally conceived. By using the viscosity solution of the Hamilton–Jacobi–Isaacs equation and introducing a rate of loss analysis for solving the singular surface they were able to find that a game optimal solution can be determined in all circumstances of the game and resolve the dilemma.
Typically when a dilemma exists, a practical approach is that players randomly choose one of the possible actions and accept losses resulting from these decisions. But here lies the catch: if there is a loss, each rational player will want to minimize it.