Theoretical Analysis Of Three Bargaining Problems

Bargaining problem and the efficiency of its solution is one of the most important issues in game theory.Bargaining theory also has lots of applications in real management problems.The main issue of the bargaining theory is to choose an outcome for all participants if they decide to cooperate.Due to fairness concerns,a reasonable outcome for a bargaining problem should satisfy some axioms or characterizations.Such a solution can result in the reduction of the sum of all players' utilities.Hence an important issue is to quantify the system efficiency loss(the price of fairness).This paper gives a lower bound of the EPM solution(extended Perles-Maschler solution),and gives an example to show that the lower bound is asymptotically tight.In bargaining problems,it is possible that some players may hold private information which other players do not know.For example,in a supply chain,the downstream retailer may hold more demand information than the upstream supplier.In previous literatures,private information is characterized by a finite set.However,private information held by participants may be very complex.This paper generalizes the bargaining solution to more general bargaining problems,i.e.,the set that characterizes the private information is more general.Many studies consider bargaining process in supply chain management,but most of them focus on the two-stage channel,and only a few of them take multi-stage channel into account.Hence,in this work,we study how the profits of the channel and all channel members are affected by the bargaining process in a multi-stage channel.Through our analyses,we obtain the following results and insights.(1)Bargaining process promote channel coordination.(2)We give a sufficient and necessary condition that all channel members gain more profits if the contracts are determined by bargaining process.(3)In previous studies,if the wholesale price contract is determined by the upstream member,then the channel efficiency decreases to 0% as the length of the channel increases to infinity;however,in our study,if the wholesale price contract is determined by bargaining process,then the channel efficiency can increase to 100% as the length of the channel increases to infinity for some situations.This paper makes the following contributions.(1)We analyze the efficiency of the EPM solution.(2)We generalize the bargaining solution to bargaining games with more general information sets.(3)We discuss the impact of the bargaining process to a multi-stage channel.