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Game Theoretic Model on a Cognitive Map

Wednesday 27 May 2015
Sergei Kulivets

4pm - 5pm, OLD 3.24, Old Building, Houghton Street 


Abstract

Some problems of complex control in fields connected with public life (i.e., social-economic, political and other fields) include a semi-structured control object. A situation appears semi-structured if the basic parameters have a qualitative (not quantitative) nature, and their values are subjective expert evaluations. Cognitive maps serve to solve control problems for semi-structured situations. The concept of a cognitive map was proposed by R. Axelrod as a digraph-based mathematical model of a decision maker belief system about some limited domain, such as a policy problem. Cognitive map nodes correspond to situation concepts. Edges are interpreted as direct causal links from one concept to another. We consider a game of players with cognitive maps (that represent players' belief systems). There are concepts that values could be controlled by some player and concepts that values have desired values for this player. The equilibrium of the game is calculated according to players’ beliefs that are represented as the hierarchy of cognitive maps. We consider the rule of changes of concept values during discrete time. Since the input data for the model is expert evaluation prone to subjectivity, it is necessary to estimate the tolerance of model results to errors in input data. For example the experts evaluate the weight of edges in the cognitive map of the player. The sign of the edge weight indicates the type of the causal link and the value of edge weight indicates the strength of the causal link. We consider the problem of the model’s tolerance to errors in input data. We also consider the problem of information control possibility when one player can manipulate the decision making process of other players through a message of false information. We illustrate all theoretical results with examples.

 

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