N-person grey game

One important assumption in the conventional cooperative game theory is that payoffs are assumed to be deterministic. In terms of the players’ cognitive ability of the realistic world, this is a very strict assumption. The classical game theory can find no way out when a particular game circumstance involves uncertainty, such as limited knowledge, small sample, and inadequate information, the payoff values of the game can only be described with interval grey numbers. The paper aims to discuss these issues.

In this study the concept of N-person grey games is proposed in which payoffs are represented with interval grey numbers opposed to the classical game theory. A straight forward solution methodology is submitted compatible to grey numbers. Then, a currency war between anonymous countries is handled and modeled as an N-Person grey game. A generic currency war scenario is developed to follow the proposed solution procedure thoroughly.

Based on the outcomes of this work, the authors can say that N-person grey game is an expansion of the classical N-person game under uncertain grey information and can be applied in more complex and uncertain environments, such as those seen in complicated currency warfare.

This study combines the grey system theory with the classic N-person game theory and sets up the N-person grey game with grey payoff functions. Based on the grey number operating methods, the grey linear programming algorithm is established to calculate and distribute benefits to the players. In this respect this study has the feature of being the pioneer in the N-person grey game area.