With in the framework of any bilevel decision problem, a leader0s decision is inrnuenced byrnthe reaction of his/her follower(s). When multiple followers who may have had a share inrndecision variables, objectives and constraints are involved in a bilevel decision problem, thernleader0s decision will be afected, not only by the reactions of the followers, but also by thernrelationships among the followers. This project rst identi es nine di erent kinds of relationshipsrn(S1toS9) among the followers. From all these kind, the project mainly focuses on arnframework for linear bilevel single follower and linear bilevel multifollower decision problems.rnFor each of the nine relation ships a corresponding linear bilevel single follower and linearrnbilevel multi-follower decision model are then developed. moreover, this project particularlyrnproposes related theories focusing on an uncooperative decision problem on which decisionrnvariables are not totally shared(i.e., S1 model), as this model linear bilevel single followerrnand linear bilevel multifollower decision problems over the nine kinds of relationships arernstated. The solution of such a problem will be in existence if the solution of the lower levelrnproblem is uniquely determined and the difculty of solving such a problem is due to therncomplementarity condition and having many solution of the lower level problem. Two solutionrnprocedures i.e., Kuhn-Tucker approach and kth best algorithm are very important torndrive an optimal solution for the uncooperative decision model even if they have their ownrnlimitations.rnKeywords: linear bilevel multifollower, kth best algorithm, KKT reformulation, lower levelrnand upper level objective functions and constraints, optimality conditions