The N-dimensional N-person chesslike game strategy analysis model

Abstract

In this research a mathematical, symmetric n-player game model, based on chess is designed. Symmetry in this context refers to players' positions with respect to each other. While the order of move naturally violates the symmetry, this problem may also be solved. The motivation for building this kind of game model stems from the difficulty of finding mathematical solutions for multi-player games in general. The number of varying factors is so huge, that finding optimal strategies is mathematically almost impossible. The best way to attempt this is to use simulation. Once the model has been built, it can be applied in many ways by using computational algorithms based on the created model. Chess in this design is the basic structure around which the model is built. The players’ weighting values can later be changed, as well as the weighting values of the pieces, in order to better reflect the variety of real-life situations. While chess is a board game, it can mirror various types of interactions between a number of different participants. Thus the game, in a larger extent, may play a role in understanding such things as politics, ecology and weather forecasting. During this research a great number of spin-off results and observations were discovered. The main objective and result of this research was, however, to create a symmetric n- person strategy game, because currently there is no simple mathematical model for symmetric n-player, strategy games.