Fuzzy Cooperative Games of Two Players under Uncertainty Conditions

摘要

Fuzzy games of two persons under uncertainty conditions are considered. For its solution the generalization of two games theory was developed based on fuzzy mathematical programing. Fuzzy antagonistic game of two persons is formulated, its mathematical model is constructed which is fuzzy linear programing problem. Fuzzy minimax theorem for optimal strategies of players is formulated (analogue of John von Neumann). Cooperative bi-matrix game under uncertainty conditions is also considered and generalization of Nash theorem for fuzzy conditions is developed. Its model was constructed and method of finding best compromise strategies of level $lpha$ was suggested. The theorem for best solutions (fuzzy Nash point) was formulated. The example of application of the suggested approach is presented and investigated