The purpose of this paper is to propose a complete theory of grey conflict analysis model based on grey game and the graph model for conflict resolution and also, to illustrate a case of “prisoner's dilemma” in the traditional grey game as an example.
Based on the theories of grey game and graph model for conflict resolution, this paper concentrates on the model of grey conflict analysis in a case of two players under the condition of symmetrical loss information. By analyzing decision makers, strategies, states, graph model and grey potential, and the number of decision makers' steps, the pure strategy Nash equilibrium is extended to grey potential‐general metarationality, grey potential‐symmetrical metarationality, and grey potential‐sequential stability. Meanwhile, the logical relationships between solutions are discussed. A specific case study is carried out to illustrate how the proposed grey conflict analysis model is used in practice.
The results in this paper indicate that more stable solutions are found when one considers the grey potential‐general metarationality, the grey potential‐symmetrical metarationality, and the grey potential‐sequential stability, and then solve the paradox of “prisoner's dilemma”.
This new grey conflict analysis model could be used to provide useful information for policy makers during existing conflicts or negotiations among parties or enterprises.
The paper succeeds in constructing a new grey conflict analysis model, in which the solution concepts are studied; and the two‐player grey game will be extended to n‐players in the near future.
