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。

An Efficient Solution of Cycle-free Graph Games Based on AT Value

This paper considers the worth of the grand coalition no less than the sum of the worth of all components for games with cycle-free communication graph structure. By introducing the property of fair distribution of the surplus, that is, the change in the average payoff of the players in a component is equal to the average payoff of the player in any other component, we propose an efficient solution of cycle-free graph games based on AT value. In addition, we provide its axiomatic characterizations combined with efficiency and component fairness. Especially, we show that the efficient solution is an element of the core for superadditive games with cycle-free communication structure which illustrates good stability. Finally, by analyzing an example applied to the efficient solution, we conclude that the more surplus to the bigger coalitions, the more payoff the key player, that is, the player which possesses the larger degree can gain.