Studies on Properties of Cooperative Games with Restrictions on Coalitions and Their Solutions

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In this research we have discussed several properties of cooperative games with restrictions on coalitions and their solutions, i.e. rational allocation schemes of profits among players. Restrictions on coalitions can be described by feasible coalition systems which consist of admissible coalitions and are the same as functions from the power set of the player set to {0,1}. We have extended the concept of feasible coalition systems in two ways.The first extension is related to the concept of graded feasible coalition systems. This extension has enabled us to deal with degrees of feasibility of coalitions. We have defined so-called restricted games from ordinary cooperative games and graded feasible coalition systems. Inheritance of some properties of cooperative games from the original cooperative games to the obtained restricted games has been established under some appropriate conditions on the games and the graded feasible coalition systems. We can also consider some solution concepts of the original games under the graded feasible coalition systems via the restricted games.The second extension leads to cooperative fuzzy games with restrictions on fuzzy coalitions. This extension can be realized through the concept of feasible fuzzy coalition sets. With this concept we can deal with feasibility of partial cooperation of players in coalitions. We have defined restricted games obtained from cooperative fuzzy games and feasible fuzzy coalition sets and discussed some properties of the restricted games. We have also focused on some special classes of cooperative fuzzy games. We have also proposed some values as solutions of cooperative fuzzy games under appropriate feasible fuzzy coalition sets together with analysis of their properties..As future researches, we are planning to refine our results and apply our theory to interesting classes of cooperative games arising from optimization problems.