考虑边流量有限的网络路径博弈问题研究

A Study of Path-Player Network Games with Limited Flow on Each Edge

考虑每条边有流量约束的网络路径博弈问题,根据收益函数单调递增的特点分析其内在零和性质,并建模为存在公共边的路径博弈模型。在寻找均衡解的过程中,首先考虑非合作的情形,在局中人风险中性的假设下,给出了求Nash均衡流量分配的标号法并证明该均衡分配的唯一性。接着进一步考虑局中人合作的可能性,给出模型求得所有局中人的整体最大收益,并基于纳什谈判模型给出目标函数为凸函数的数学模型确定唯一收益分配方案。事实上,该方案是对剩余价值的平均分配。最后给出一个算例,验证本文理论和方法的可行性。

This paper concerns path-player network games in the presence of limited flow on each edge.Considering the feature of monotonically increasing of the revenue function of each player,we examine the properties of the discussed game and formulate it by a path-player game model with common edges.In the process of searching equilibrium solutions,we first analyze the noncooperative situation.Under the assumption that all the players are risk neutral,we show an approach to find the Nash equilibrium and additionally demonstrate that the equilibrium flow allocation determined by the approach is unique.We further consider the possibility of cooperation among the players,propose a model to maximize the overall revenue,and then determine the unique allocation solution by modifying the Nash bargaining model.In fact,this solution is the equal division of surplus revenues.Finally we present a numerical illustration to verify the feasibility of the methods proposed in this paper.