基于目标端影响模型与次模性的预算分配博弈问题分析  

Analysis of Budget Allocation Game Based on Target-Side Influence Model and Submodular

作　　者：农庆琴[1] 王媛媛 Nong Qingqin;Wang Yuanyuan(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2023年第2期153-158,共6页Periodical of Ocean University of China

基　　金：山东省自然科学基金项目(ZR2019MA052);国家自然科学基金项目(11871442);中央高校基本科研基金项目(201961003,201861001)资助。

摘　　要：为了解决品牌商如何通过媒体频道分配预算(投放广告)进行有效营销这一问题,本文研究了目标端影响模型下的预算分配问题。首先,将基于目标端影响模型的单个品牌商的预算分配问题扩展到整数格上,证明该优化问题的目标函数是整数格上的单调次模函数;其次,探讨了基于目标端影响模型的多个广告商的预算分配博弈问题,证明预算分配博弈为势博弈;最后,证明了基于目标端影响模型的预算分配博弈的无秩序代价至多为2。In order to study the problem of how to allocate budget(advertising)for marketing through media channels,this paper studies the budget allocation problem under the target side impact model.Firstly,the budget allocation problem of a single brand is extended to an integer lattice,and it is proved that the optimization broblem is a monotone submodular function maximization over an integer lattice.Secondly,this paper discusses the budget allocation game of multiple advertisers based on the target side impact model,and proves that the channel advertising budget allocation game is a potential game.Finally,it is proved that the price of anarchy of budget allocation game is at most 2.

关 键 词：势博弈 预算分配 纳什均衡 目标端影响模型 无秩序代价 

分 类 号：O225[理学—运筹学与控制论]