The Shapley value: Endogenous formation of links between players and of coalitions: an application of the Shapley value
The Shapley value: Endogenous formation of links between players and of coalitions: an application of the Shapley value
复制标题
沙普利值：参与者和联盟之间联系的内生形成：沙普利值的应用
DOI：
10.1017/cbo9780511528446.013
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
R. Myerson
中科院分区：
文献类型：
--
作者：
R. Aumann;R. Myerson
考虑由$$ v(S) = \left\{ \begin{array}{l} 0\quad if{\kern 1pt} \left| S \right| = 1, \\ 60\quad if{\kern 1pt} \left| S \right| = 2, \\ 72\quad if{\kern 1pt} \left| S \right| = 3, \\ \end{array} \right. $$定义的玩家集（1,2,3）上的联盟博弈v，其中|表示玩家inS的数量。大多数合作解决方案概念“预测”（或假设）所有参与者的联盟{1、2、3}将形成，并以某种适当的方式分配收益72。假设参与人1和p2在没有P3的情况下相遇。毫无疑问，他们将迅速抓住机会组建联合政府，并各自获得30英镑的收益。尽管效率低下，但这种情况还是会发生。原因是，如果piandp2邀请ep3加入谈判，那么三个参与者将发现自己处于有效对称的角色，预期结果将是{24,24,24}。p1p2不想冒险提供4个toP3（并将剩下的68个分给他们自己），因为他们会意识到oncep3被邀请参加谈判，情况变得“非常开放”——任何事情都可能发生。{}
Consider the coalitional game v on the player set (1,2,3) defined by $$ v(S) = \left\{ \begin{array}{l} 0\quad if{\kern 1pt} \left| S \right| = 1, \\ 60\quad if{\kern 1pt} \left| S \right| = 2, \\ 72\quad if{\kern 1pt} \left| S \right| = 3, \\ \end{array} \right. $$ were |S| denotes the number of players inS. Most cooperative solution concepts “predict” (or assume) that the all-player coalition {1, 2, 3} will form and divide the payoff 72 in some appropriate way. Now suppose thatP1(player 1) andP2happen to meet each other in the absence of P3. There is little doubt that they would quickly seize the opportunity to form the coalition {1, 2} and collect a payoff of 30 each. This would happen in spite of its inefficiency. The reason is that if PiandP2were to inviteP3to join the negotiations, then the three players would find themselves in effectively symmetric roles, and the expected outcome would be {24,24,24}. P1andP2would not want to risk offering, say, 4 toP3(and dividing the remaining 68 among themselves), because they would realize that onceP3is invited to participate in the negotiations, the situation turns “wide open” — anything can happen.