<p>Complex information systems often operate in cooperative environments where participants’ involvement is uncertain and may occur at multiple probabilistic participation levels. The purpose of this paper is to introduce a congruent optimization approach for cooperative games with probabilistic participation levels. We first define a new characteristic function with probabilistic participation proportional forms of cooperative games with probabilistic participation levels. The congruent contribution excess of players is introduced. An optimization problem is constructed by minimizing the variance of the congruent contribution excess of players. A new solution named the congruent value is proposed. Then, we establish the axiomatization of the congruent value. An interesting result that shows the relationship between the congruent value and the equal division value is explored. Considering the influence of the probabilistic participation level of players, the probabilistic weighted congruent value is developed. The axiomatization of the probabilistic weighted congruent value is provided. Some ideal properties of the proposed value are discussed.</p>

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A congruent optimization approach for cooperative games based on the cross-dimensional participation information system

  • Jun Guo,
  • Jian Lin

摘要

Complex information systems often operate in cooperative environments where participants’ involvement is uncertain and may occur at multiple probabilistic participation levels. The purpose of this paper is to introduce a congruent optimization approach for cooperative games with probabilistic participation levels. We first define a new characteristic function with probabilistic participation proportional forms of cooperative games with probabilistic participation levels. The congruent contribution excess of players is introduced. An optimization problem is constructed by minimizing the variance of the congruent contribution excess of players. A new solution named the congruent value is proposed. Then, we establish the axiomatization of the congruent value. An interesting result that shows the relationship between the congruent value and the equal division value is explored. Considering the influence of the probabilistic participation level of players, the probabilistic weighted congruent value is developed. The axiomatization of the probabilistic weighted congruent value is provided. Some ideal properties of the proposed value are discussed.