Game-theoretic Model on a Cognitive Map and its Tolerance to Errors in Input Data

Abstract

Some problems of complex control in the fields connected with public life (i.e., social-economic, political and other fields) include semistructured control object. Situation appears semistructured if the basic parameters have qualitative (not quantitative) nature, and their values are subjective expert evaluations. Cognitive maps serve to solve control problems for semistructured situations. Cognitive map is a model representing knowledge of the expert (or a group of experts) regarding situation; this model is described in the form of weighted directed graph. The nodes of cognitive map correspond to those concepts being employed to describe the situation. The concept may be treated as a variable (for instance, “national defence capacity”) which may have different values, such as “high,” “low” and so on. Weighted arc is interpreted as direct cause-effect relationship between two concepts. Suppose several decision-makers (agents) take part in the process of decision making in an semistructured situation given that the utility of each of them depends both on his self actions and the actions of the others, than interactions of the agents can be seen as a game on the cognitive map. In the game cognitive map represents a model of semistructured control object and clearly describe the dynamics of the situation. The use of cognitive maps in the game gives more detailed and visual modeling of the conflict environment in the form of simple causal links, so as to describe the goals and strategies of the agents in terms of the environment which makes it more convenient to model the real conflicts adequately. Since the input data for the model are expert evaluation prone to subjectiveness, it is necessary to estimate the tolerance of model results to errors in input data. Experts evaluate the “importance percentage” of a target concept compared the others target concepts and the weight of edges in cognitive map. The sign of edge weight indicates the type of the causal link and the value of edge weight indicates the strength of the causal link. In this paper we consider the problem of model tolerance to errors in input data and illustrate it on the material of conflict of interests between Russia and Norway in the Barents Sea.