基于平均树值的无圈图博弈有效解

本文对无圈图博弈进行了研究,考虑了大联盟收益不小于各分支收益之和的情况。通过引入剩余公平分配性质,也就是任意两个分支联盟的平均支付变化相等,给出了一个基于平均树值的无圈图博弈有效解。同时,结合有效性和分支公平性对该有效解进行了刻画。特别地,若无圈图博弈满足超可加性时,证明了该有效解一定是核中的元素,说明此时的解是稳定的。最后,通过一案例分析了该有效解的特点,即越大的分支分得的剩余越多,并且关键参与者,也就是具有较大度的参与者可获得相对多的支付。     

Elementary Properties of Cycle-free Partial Orders and their Automorphism Groups

A classification was given by Creed, Truss, and Warren of all the countable k-CS-transitive cycle-free partial orders for k3. Here the elementary theories of these structures and their automorphism groups are examined, and it is shown that in many cases we can distinguish the structures or their groups by means of their first- or second-order properties. The small index property is established for weakly 2-transitive trees, and for several classes of cycle-free partial orders.