Solution sets of cooperative games and a cooperative game with no solution

In this thesis, some set-valued and single-valued solution concepts in cooperative game theory are examined in general. The core and the core cover solution, which are set valued solutions, are introduced and explained with relevant examples. Among the single valued solution concepts, the Shapley value and the 𝜏-value are introduced and explained with appropriate examples. In the final section of the thesis, before discussing a game with no solution, definitions related to dominance and solution concepts in cooperative games are provided. While proving the absence of a solution for the given game, certain sets that will aid in the proof are introduced and illustrated with graphs. Finally, by assuming that a solution exists, a contradiction is obtained by showing that the assumed solution is inconsistent with the concepts of dominance and the solution set, proving that no solution exists.