Exploring the Benefits of Representing Multiplayer Game Data in a Coordinate System

In the realm of game theory, a range of mathematical approaches exists for the representation of game data, with the extensive form (depicted as a game tree) and the normal form (illustrated as a payoff matrix) standing out as the most prevalent. However, a significant drawback associated with these approaches is their limited scalability. As the number of players or their strategic options increases, these techniques progressively lose their feasibility and become less practical for meaningful analysis. The present work proposes an alternative approach that significantly enhances the representation of data in two- or three-player games. Within this framework, the conventional payoff matrix is substituted with a payoff coordinate system, employing a coordinate plane for two-player games and a coordinate space for three-player games. This approach offers numerous advantages when compared to other methods. For instance, the Nash equilibrium can be readily identified within a game without requiring an extensive duration to exhaustively examine all strategies for its determination. By employing this approach, the representation of game data becomes more convenient and efficient, making it easier to analyze and comprehend the underlying strategies employed by players.