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数据分析与知识发现  2018 , 2 (6): 13-24 https://doi.org/10.11925/infotech.2096-3467.2017.1101

研究论文

激励机制下图书馆信息安全管理的投入意愿研究*——基于演化博弈的视角

朱光, 丰米宁, 张薇薇

南京信息工程大学管理工程学院 南京 210044

Incentive Investments on Information Security for Libraries: An Evolutionary Game-theory Approach

Zhu Guang, Feng Mining, Zhang Weiwei

School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

中图分类号:  G250

通讯作者:  通讯作者: 朱光, ORCID:0000-0003-4749-8603, E-mail: guangguang4992@sina.com

收稿日期: 2017-11-5

修回日期:  2018-03-7

网络出版日期:  2018-06-25

版权声明:  2018 《数据分析与知识发现》编辑部 《数据分析与知识发现》编辑部

基金资助:  *本文系国家自然科学基金项目“信息生命周期视角下的大数据隐私风险评估和溯源问责机制研究”(项目编号: 71503133)、南京信息工程大学科学技术史研究院开放课题“信息生命周期视角下的图博档多媒体资源安全策略研究”(项目编号: 2017KJSKT006)和南京信息工程大学本科生优秀毕业论文(设计)支持计划项目的研究成果之一

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摘要

目的】分析不同成本和收益条件下图书馆信息安全管理的投入意愿, 解决投入过程中可能存在的“搭便车”问题, 提高图书馆信息安全管理的水平和效率。【方法】运用演化博弈理论, 设计由图书馆和技术研发企业组成的博弈主体, 探究双方在图书馆信息安全管理过程中的投入意愿。根据不同博弈策略的收益和成本, 计算博弈双方的支付矩阵, 分析信息安全投入的演化稳定策略。据此设计第三方激励机制, 以增强博弈双方的投入意愿。【结果】图书馆与技术研发企业的投入意愿与投入收益增率、投入成本、“搭便车”所获收益密切相关。当投入收益增率较小时, 博弈双方不会选择“高效投入”。随着投入收益增率逐渐变大, 博弈双方选择“高效投入”的概率随之提高, 并会出现多种演化稳定策略。【局限】未能设计非线性收益函数; 未能考虑其他影响演化稳定策略的因素(如用户意愿、广告因素等)。【结论】通过分析“收益-成本”因素对信息安全管理投入意愿的影响, 促进图书馆信息安全管理的发展, 并提高管理水平。

关键词: 图书馆 ; 信息安全管理 ; 投入意愿 ; 激励 ; 演化博弈

Abstract

[Objective] This paper analyzes the library’s investment on information security from the benefit and cost perspectives, aiming to improve the effectiveness and efficiency of library security management. [Methods] First, we used the evolutionary game theory to define two players: library and technical enterprise. Then, we explored the intentions of investments on information security. Third, we analyzed the benefits and costs of investments, the payoff matrices and evolutionarily stable strategies (ESS). Finally, we designed an incentive mechanism to enhance the investment on information security. [Results] The investments from libraries and enterprises were correlated with benefit growth and cost reduction. If the benefit growth was small, the game players are less likely to invest. Once the profit growth became big, the game players tend to invest and then generated different strategies. [Limitations] We did not design the nonlinear profit function. Other factors, such as user’s demands and advertisement effects should also be included. [Conclusions] This study promotes the development of information security management in library.

Keywords: Library ; Information Security Management ; Investment Desire ; Incentive ; Evolutionary Game

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朱光, 丰米宁, 张薇薇. 激励机制下图书馆信息安全管理的投入意愿研究*——基于演化博弈的视角[J]. 数据分析与知识发现, 2018, 2(6): 13-24 https://doi.org/10.11925/infotech.2096-3467.2017.1101

Zhu Guang, Feng Mining, Zhang Weiwei. Incentive Investments on Information Security for Libraries: An Evolutionary Game-theory Approach[J]. Data Analysis and Knowledge Discovery, 2018, 2(6): 13-24 https://doi.org/10.11925/infotech.2096-3467.2017.1101

1 引 言

随着数字处理和网络通信技术的飞速发展, 各类数字资源(图像、音频、视频)的传输、存储和共享更为便捷。图书馆作为传统的文献收藏和信息服务机构, 纷纷将自身的馆藏资源数字化, 并借助网络平台进行共享和整合[1]。图书馆数字资源共享和融合在方便用户获取信息资源的同时, 也使得数字资源的安全性受到前所未有的冲击。在网络共享和服务融合环境下, 人们可以不受限制地编辑、拷贝和传播数字资源, 这给一些团体和个人实施非法行为带来可乘之机。因此, 如何建立一个完善、有效的图书馆数字资源信息安全管理机制成为重要课题。

目前数字资源的信息安全研究主要集中于版权保护[2,3]、内容完整性认证[4]、访问控制[5]等技术领域, 从哈希函数、密码学认证以及数字水印等技术角度展开。然而, 从经济学角度分析, 图书馆数字资源的安全管理需要多个主体(如图书馆、技术研发企业、政府决策部门等)共同协作, 并在人力、经济、技术上进行持续性投入, 是一个多主体的长期决策过程。基于贝叶斯博弈、差分博弈、非合作博弈以及不完全博弈的信息安全投入决策难以在长期博弈过程中获得最优解, 与此同时, 也鲜有研究考虑到第三方激励机制的影响。

基于此, 本文从演化博弈的视角出发, 计算不同参与主体信息安全的投入成本和收益, 探究不同条件下图书馆信息安全管理的投入意愿。并分析参与主体投入行为的演化路径和稳定策略, 对于更好地开展图书馆资源共享和信息安全管理工作具有一定的参考意义。

2 研究现状

目前国内外关于数字资源的信息安全技术研究主要集中在版权保护、内容认证和访问控制等技术领域, 主要运用数字水印、数字签名、密码认证以及生物特征识别等技术方法。版权保护是为了保护信息资源著作权和知识产权而提出的一种有效方案, Ahmad等[6]提出一种基于动态MPEG编码的数字水印算法, 可以对数字图书馆共享的视频资源进行有效的版权鉴别, 并设计实践应用框架;朱光等[7]结合图博档视频资源的特征, 针对网络环境下版权保护的实时性需求, 提出一种基于DCT(Discrete Cosine Transform)系数量化调制的视频水印算法, 有效地解决了现有视频水印技术在执行效率和实时性上存在的不足。针对图书馆数字资源的内容认证研究, 由于基于哈希函数的技术方案安全性较低, 也无法确定数字资源遭受篡改的位置[8], 研究学者将半脆弱水印技术应用于数字资源的内容认证中, Qi等[9]提出一种数字图像的内容认证方案, 利用修改图像量化系数嵌入半脆弱水印, 并通过水印信息的提取完成认证; Satoshi等[10]提出一种针对二维条码的半脆弱水印认证算法, 将水印标识嵌入至条码图像的高频小波系数中, 检测系数是否改动以实现条码内容认证。针对图书馆数字资源的访问控制研究, Kabi等[11]提出基于角色意图的访问控制模型, 该模型在基于角色访问控制模型的基础上增加对访问意图的支持, 实现对数据隐私的细粒度保护; 徐文哲[12]针对图博档数字化融合服务的信任协商模型, 深入探讨访问控制策略内部结构的设计、访问控制策略树的构造以及标记和遍历过程, 在此基础上设计访问控制情境下的信任本体概念模型。

在信息安全投入和管理决策领域, Gordon等[13]提出一个基于博弈论的信息安全最优投入模型, 研究结果表明信息系统脆弱性和数据泄露风险决定信息安全的投入决策; Cavusoglu等[14]运用博弈论分析信息安全的攻防问题, 提出防守方的信息安全投入策略取决于黑客攻击造成的损失, 攻击方的信息安全攻击决策取决其被捕捉的概率; Fielder等[15]运用贝叶斯博弈, 模拟中小型企业与黑客之间的信息安全多阶段决策过程, 以分析信息安全的投入预算; Gao等[16]运用差分博弈研究信息安全投入决策与信息共享之间的关系, 研究结果表明最优信息安全投入策略与市场合作存在紧密关联; Liu等[17]研究相似企业信息安全策略与市场竞争的关系, 结果表明, 两家相似企业的信息安全投入决策无法同时达到最优, 只能获得次优(Sub-Optimal)策略; 顾建强等[18]研究非合作博弈下信息系统安全投入的最优策略选择, 在此基础上分析投入效率参数、黑客学习能力、传染风险对信息系统脆弱性及信息系统安全投入决策的影响。

综合来看, 图书馆数字资源的信息安全投入与管理是一个涉及多个环节, 并应用诸多技术方法的复杂过程, 现有研究主要关注其技术实现和应用分析等内容。然而, 信息安全管理并不仅仅是一个技术难题, 现实条件下, 参与主体往往从经济学的角度对自身收益和支出进行衡量, 做出管理投入决策。

回顾已有的研究成果, 基于贝叶斯博弈、差分博弈、非合作博弈以及不完全博弈的决策分析均以博弈主体的理性经济假设为前提条件, 定义博弈主体的策略空间确定并可以预知, 这显然与图书馆信息安全投入的实际情形不相符。国内以政府为主导, 图书馆与技术研发企业共同参与的信息安全投入和管理模式, 以及市场信息不对称的现状, 决定博弈主体需要在不断学习和调整过程中逐渐实现最优决策。演化博弈理论[19]对于博弈主体的有限理性假设以及种群自然选择、优胜劣汰的演化机制, 能更为合理地描述上述情形。因此, 本文通过构建演化博弈模型, 分析不同参与主体的信息安全投入成本和收益, 探究不同参数下图书馆信息安全管理的投入意愿, 并运用Matlab进行数值仿真, 模拟博弈主体在信息安全投入过程中的演化路径与稳定策略。

3 模型构建

3.1 问题描述与参数设定

在图书馆信息安全管理过程中, 参与主体选择信息安全投入的前提条件是收益最大化, 只有投入收益大于投入成本时, 参与主体才会采取积极的投入策略, 否则“机会主义”、“搭便车”等问题就会产生[20]。然而, 由于技术条件、场馆规模、投资环境、信息安全意识等方面的差异性和复杂性, 参与主体都是有限理性 的[21], 利用传统的贝叶斯博弈模型[22]、差分博弈模 型[23]、不完全动态博弈模型[24]难以在单次博弈决策中获得最优均衡解。

演化博弈认为博弈主体都是有限理性的, 需要通过试错和对较高收益策略进行模仿, 从而达到一种稳定均衡状态[25]。演化博弈的基本思想是: 假设存在一个较大的群体A, 选择某一特定策略M, 同时存在一个较小的异样群体B, 选择不同策略N。当群体A侵入群体B形成一个混合群体时, 如果小群体B在混合群体中获得的收益大于群体A的原有收益, 则小群体B会影响到大群体A的策略选择; 反之, 群体B逐渐倾向于与大群体A选择相同的策略。最后, 如果大群体不被任何小群体影响策略的选择, 则认为该群体达到了稳定状态, 称该策略为演化稳定策略(Evolutionarily Stable Strategy, ESS)[26]

根据上述问题描述, 本文从图书馆信息安全管理的投入成本和收益视角, 运用演化博弈理论对参与主体的投入意愿进行分析和探讨。为便于模型构建和参数计算, 提出以下假设。

(1) 图书馆的信息安全管理需要不同主体协同合作, 本文定义博弈过程中的参与主体为{图书馆, 技术研发企业}。两者均为有限理性的主体, 其行为选择依赖于博弈策略带来的收益, 在演化博弈过程中博弈主体可以根据收益情况改变其行为策略。图书馆(L)负责设备购入、软件升级和信息安全意识培训等工作; 技术研发企业(E)负责算法设计、软件开发和硬件调试等工作。

(2) 定义博弈双方的策略空间为{高效投入, 低效投入}, “高效投入”指参与主体具有较强的信息安全意识, 主动履行职责, 制定切实可行的信息安全管理战略, 持续性投入一定的人力、经济和技术成本, 建立安全、有效的图书馆数字服务平台。“低效投入”是指由于信息安全投入带来的收益较小, 不足以覆盖投入成本, 参与主体敷衍了事, 或者不愿意长期对图书馆的信息安全管理进行投入。

(3) 当博弈双方中某一方选择“高效投入”, 另一方选择“低效投入”时, 可能会产生“机会主义”效应, 选择“低效投入”的一方会获得“搭便车”带来的额外收益。

(4) 当“机会主义”和“搭便车”效应形成时, 可以引入第三方激励机制, 对选择“高效投入”的主体给予补偿, 对选择“低效投入”的主体给予惩罚, 从而促成博弈双方共同选择“高效投入”策略, 实现持续性投入, 保障图书馆信息资源的安全。

3.2 参数设定与收益分析

根据上述假设, 本文定义模型的相关参数如表1所示。

表1   模型相关参数

   

符号意义和说明
L图书馆
E技术研发企业
PL博弈双方同时选择“低效投入”, 图书馆所获得的收益, PL > 0
PE博弈双方同时选择“低效投入”, 技术研发企业所获得的收益, PE > 0
DL图书馆选择“高效投入”时的投入成本, CL > 0
CE技术研发企业选择“高效投入”时的投入成本, CE>0
ξL图书馆“搭便车”所获得的额外收益, ξL >PL>0
ξE技术研发企业“搭便车”所获得的额外收益, ξE >PE>0
a0图书馆选择“高效投入”, 技术研发企业选择“低效投入”时, 图书馆的投入增益系数, a0>0
a1博弈双方都选择“高效投入”时, 图书馆的投入增益系数, a1> a0>0
b0图书馆选择“低效投入”, 技术研发企业选择“高效投入”时, 技术研发企业的投入增益系数, b0>0
b1博弈双方都选择“高效投入”时, 技术研发企业的投入增益系数, b1> b0>0

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根据上述参数, 博弈双方选择不同策略的收益包括以下情况。

(1) 当图书馆和技术研发企业均选择“低效投入”时, 会出现数据丢失、隐私泄露、信誉下降等问题, 但收益减损是一个长期过程, 在未来一段时期内, 博弈双方仍然能够获取一定收益, 定义图书馆选择“低效投入”获取的收益为PL, 技术研发企业选择“低效投入” 获取的收益为PE

(2) 若只有图书馆选择“高效投入”, 通过提高信息安全意识, 制定信息安全规范, 以提高图书馆的信息安全管理水平。在此情况下, “高效投入”带给图书馆的收益包括信息安全管理水平提高, 用户数量增多, 信息服务声誉提高等, 收益可以定义为$(1+{{a}_{0}}){{P}_{L}}-{{C}_{L}}$。此时, 若技术研发企业选择“低效投入”, 会形成“搭便车”效应, 技术研发企业获取了比双方都选择“低效投入”时更高的收益ξE

(3) 若只有技术研发企业选择“高效投入”, 通过设计和开发安全性能更加优越的软硬件设施, 以提高图书馆的信息安全管理效率。在此情况下, “高效投入”带给技术研发企业的收益包括获得行业竞争优势和更大的市场份额, 借助安全性更高的产品和服务促成良性循环, 提高企业声誉, 形成市场惯性, 推动企业规模的扩大和发展, 其收益定义为$(1+{{b}_{0}}){{P}_{E}}-{{C}_{E}}$。此时, 若图书馆选择“低效投入”, 同样会形成“搭便车”效应, 图书馆获取了技术研发企业“高效投入”所带来的隐形收益ξL

(4) 当图书馆和技术研发企业都选择“高效投入”时, 图书馆信息安全管理得到多重改善, 在此情况下, 博弈双方的收益为$(1+{{a}_{1}}){{P}_{L}}-{{C}_{L}}$和$(1+{{b}_{1}}){{P}_{E}}-{{C}_{E}}$。

基于此, 博弈双方的支付矩阵如表2所示。

表2   支付矩阵

   

LE
高效投入低效投入
高效投入(1+a1)PL-CL, (1+b1)PE-CE(1+a0)PL-CL, ξE
低效投入ξL, (1+b0)PE-CEPL, PE

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4 演化模型分析

4.1 模型均衡点

假设在图书馆群体中, 选择“高效投入”策略的比例为$x(0\le x\le 1)$, 则采取“低效投入”策略的比例为1-x; 在技术研发企业群体中, 采取“高效投入”策略的比例为$y(0\le y\le 1)$, 则采取“低效投入”策略的比例为1-y

定义图书馆选择“高效投入”和“低效投入”的期望收益B1YB1N及平均期望收益$\overline{{{B}_{1}}}$分别如公式(1)-公式(3)所示。

${{B}_{1Y}}=y[(1+{{a}_{1}}){{P}_{L}}-{{C}_{L}}]+(1-y)[(1+{{a}_{0}}){{P}_{L}}-{{C}_{L}}] $ (1)

${{B}_{1N}}=y{{\xi }_{L}}+(1-y){{P}_{L}}$ (2)

$\overline{{{B}_{1}}}=x{{B}_{1Y}}+(1-x){{B}_{1N}} $ (3)

根据Malthusian模型[27], 复制动态方程如公式(4)所示。

$\begin{align}& G(x)=\frac{dx}{dt}=x({{B}_{1Y}}-\overline{{{B}_{1}}}) \\ & =x(1-x)\{{{a}_{0}}{{P}_{L}}-{{C}_{L}}-[{{\xi }_{L}}-({{a}_{1}}-{{a}_{0}}+1){{P}_{L}}]y\} \\ \end{align}$ (4)

同理, 技术研发企业选择“高效投入”和“低效投入”策略的期望收益B2YB2N及平均收益$\overline{{{B}_{2}}}$分别如公式(5)-公式(7)所示。

${{B}_{2Y}}=x[(1+{{b}_{1}}){{P}_{E}}-{{C}_{E}}]+(1-x)[(1+{{b}_{0}}){{P}_{E}}-{{C}_{E}}] $ (5)

${{B}_{2N}}=x{{\xi }_{E}}+(1-x){{P}_{E}}$ (6)

$\overline{{{B}_{2}}}=x{{B}_{2Y}}+(1-x){{B}_{2N}} $ (7)

复制动态方程如公式(8)所示。

$\begin{align} & G(y)=\frac{dy}{dt}=y({{B}_{2Y}}-\overline{{{B}_{2}}}) \\ & =y(1-y)\{{{b}_{0}}{{P}_{E}}-{{C}_{E}}-[{{\xi }_{E}}-({{b}_{1}}-{{b}_{0}}+1){{P}_{E}}]x\} \\ \end{align}$ (8)

令$(\frac{dx}{dt},\frac{dy}{dt})=(0,0)$, 可得到演化模型的5个均衡点为(0, 0)、(0, 1)、(1, 0)、(1, 1)和(A, B), (A, B)定义为$(\frac{{{b}_{0}}{{P}_{E}}-{{C}_{E}}}{{{\xi }_{E}}-({{b}_{1}}-{{b}_{0}}+1){{P}_{E}}},\frac{{{a}_{0}}{{P}_{L}}-{{C}_{L}}}{{{\xi }_{L}}-({{a}_{1}}-{{a}_{0}}+1){{P}_{L}}})$。

4.2 均衡点的稳定性分析

演化均衡点的稳定性可以通过雅克比矩阵的局部稳定分析得出[19], 依次求G(x)和G(y)的偏导数, 得到雅克比矩阵如公式(9)所示。

$J=\left[ \begin{align} & \frac{\partial G(x)}{\partial x}\text{ }\frac{\partial G(x)}{\partial y} \\ & \frac{\partial G(y)}{\partial x}\text{ }\frac{\partial G(y)}{\partial y} \\ \end{align} \right]$$=\left[ \begin{align} & {{a}_{11}}\text{ }{{a}_{12}} \\ & {{a}_{21}}\text{ }{{a}_{22}} \\ \end{align} \right] $ (9)

若矩阵元素满足以下两个条件:

(1) $trJ={{a}_{11}}+{{a}_{22}}<0$

(2) $detJ=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\\end{matrix} \right]={{a}_{11}}{{a}_{22}}-{{a}_{12}}{{a}_{21}}>0$

则复制动态方程的均衡点就是演化稳定策略。根据上述条件, 可以得到5个局部均衡点(0, 0)、(0, 1)、(1, 0)、(1, 1)、(A, B)的具体取值, 如表3所示。

表3   局部均衡点的具体取值

   

均衡点${{a}_{11}}$${{a}_{12}}$${{a}_{21}}$${{a}_{22}}$
(0, 0)a0PL-CL00b0PE-CE
(0, 1)a1PL-CL-ξL+PL00-(b0PE-CE)
(1, 0)-(a0PL-CL)00b1PE-CE-ξE+PE
(1, 1)-(a1PL-CL-ξL+PL)00-(b1PE-CE-ξE+PE)
(A, B)0a12(A, B)a21(A, B)0

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显然, 在均衡点(A, B)处有a11+a22=0, 不满足条件(1), 因此均衡点(A, B)肯定不是演化稳定策略。综合分析其余4个均衡点的取值, 当图书馆和技术研发企业选择“高效投入”策略时的收益增率a0a1b0b1所在区间发生变化时, 各个均衡点的演化策略也会随之变化, 演化相位图如图1所示。

图1   演化相位图

   

(1) 演化稳定策略1: 当图书馆的投入收益增率满足$0<{{a}_{0}}<\frac{{{C}_{L}}}{{{P}_{L}}}$, ${{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$, 且技术研发企业的投入收益增率满足$0<{{b}_{0}}<\frac{{{C}_{E}}}{{{P}_{E}}}$, ${{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$时, (0, 0)是演化稳定点, (0, 1)和(1, 0)是鞍点, (1, 1)是不稳定点。博弈双方的演化稳定策略为(低效投入, 低效投入)。

证明1: 根据上述收益增率的条件, 博弈双方选择“高效投入”的收益如下。

$(1+{{a}_{0}}){{P}_{L}}-{{C}_{L}}<(1+\frac{{{C}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{P}_{L}}$

$(1+{{a}_{1}}){{P}_{L}}-{{C}_{L}}<(1+\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{\xi }_{L}}$

$(1+{{b}_{0}}){{P}_{E}}-{{C}_{E}}<(1+\frac{{{C}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{P}_{E}}$

$(1+{{b}_{1}}){{P}_{E}}-{{C}_{E}}<(1+\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{\xi }_{E}}$

可以看出, 当博弈双方仅有一方选择“高效投入”时, 其收益小于双方都选择“低效投入”的收益; 当博弈双方都选择“高效投入”时, 其收益小于“搭便车”的收益。在此情况下, 最终的演化稳定策略为(低效投入, 低效投入), 演化趋势如图1(a)所示。

(2) 演化稳定策略2: 当图书馆的投入收益增率满足$0<{{a}_{0}}<\frac{{{C}_{L}}}{{{P}_{L}}}$, ${{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$, 且技术研发企业的投入收益增率满足$\frac{{{C}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$时, (0, 1)是演化稳定点, (0, 0)和(1, 0)是鞍点, (1, 1)是不 稳定点。博弈双方的演化稳定策略为(低效投入, 高效投入)。

证明2: 根据上述条件, 图书馆的收益保持不变, 技术研发企业选择“高效投入”的收益如下。

$(1+{{b}_{0}}){{P}_{E}}-{{C}_{E}}>(1+\frac{{{C}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{P}_{E}}$

$(1+{{b}_{1}}){{P}_{E}}-{{C}_{E}}<(1+\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{\xi }_{E}}$

由证明1可知, 图书馆仍然倾向于选择“低效投入”。此时, 若技术研发企业选择“高效投入”, 其收益大于双方都选择“低效投入”的收益。因此, 最终的演化稳定策略为(低效投入, 高效投入), 演化趋势如图1(b)所示。

(3) 演化稳定策略3: 当图书馆的投入收益增率满足$\frac{{{C}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$, 且技术研发企业的投入收益增率满足$0<{{b}_{0}}<\frac{{{C}_{E}}}{{{P}_{E}}}$, ${{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$时, (1, 0)是演化稳定点, (0, 0)和(0, 1)是鞍点, (1, 1)是不稳定点。博弈双方的演化稳定策略为(高效投入, 低效投入)。

证明3: 根据上述条件, 图书馆选择“高效投入”的收益如下。

$(1+{{a}_{0}}){{P}_{L}}-{{C}_{L}}>(1+\frac{{{C}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{P}_{L}}$

$(1+{{a}_{1}}){{P}_{L}}-{{C}_{L}}<(1+\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{\xi }_{L}}$

同理, 由于技术研发企业仍然倾向于选择“低效投入”, 若图书馆选择“高效投入”, 其收益大于双方都选择“低效投入”的收益。因此, 最终的演化稳定策略为(高效投入, 低效投入), 演化趋势如图1(c)所示。

(4) 演化稳定策略4: 当图书馆的收益增率满足$\frac{{{C}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$, 技术研发企业的收益增率满足$\frac{{{C}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$时, 可能形成“搭便车”效应, (0, 1)和(1, 0)是演化稳定点, (0, 0)和(1, 1)是不稳定点, (A, B)是鞍点, 博弈双方的演化稳定策略为(高效投入, 低效投入)或(低效投入, 高效投入)。

证明4: 根据上述条件, 博弈双方选择“高效投入”的收益如下。

$(1+{{a}_{0}}){{P}_{L}}-{{C}_{L}}>(1+\frac{{{C}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{P}_{L}}$

$(1+{{a}_{1}}){{P}_{L}}-{{C}_{L}}<(1+\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{\xi }_{L}}$

$(1+{{b}_{0}}){{P}_{E}}-{{C}_{E}}>(1+\frac{{{C}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{P}_{E}}$

$(1+{{b}_{1}}){{P}_{E}}-{{C}_{E}}<(1+\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{\xi }_{E}}$

可以看出, 当博弈双方仅有一方选择“高效投入”时, 其收益大于双方都选择“低效投入”的收益; 当博弈双方都选择“高效投入”时, 其收益小于“搭便车”的收益。因此, 在演化过程中, 若博弈双方有一方观察到另一方选择“高效投入”, 则其在演化过程中会调整其策略, 选择“低效投入”; 同理, 若博弈双方有一方观察到另一方选择“低效投入”, 则其为了最大化收益, 在演化过程中会选择“高效投入”。因此, 最终的演化稳定策略为(低效投入, 高效投入)或(高效投入, 低效投入), 演化趋势如图1(d)所示。

(5) 演化稳定策略5: 当图书馆的收益增率和技术研发企业的收益增率满足$\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}$和$\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}$时, (1, 1)是演化稳定点, (0, 1)和(1, 0)是鞍点, (0, 0)是不稳定点。博弈双方的演化稳定策略为(高效投入, 高效投入)。

证明5: 根据上述条件, 博弈双方选择“高效投入”的收益如下。

$(1+{{a}_{0}}){{P}_{L}}-{{C}_{L}}>(1+\frac{{{C}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{P}_{L}}$

$(1+{{a}_{1}}){{P}_{L}}-{{C}_{L}}>(1+\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}){{P}_{L}}-{{C}_{L}}={{\xi }_{L}}$

$(1+{{b}_{0}}){{P}_{E}}-{{C}_{E}}>(1+\frac{{{C}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{P}_{E}}$

$(1+{{b}_{1}}){{P}_{E}}-{{C}_{E}}>(1+\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}){{P}_{E}}-{{C}_{E}}={{\xi }_{E}}$

可以看出, 博弈双方选择“高效投入”的收益既大于“低效投入”的收益, 也大约“搭便车”的收益。因此, 最终的演化稳定策略为(高效投入, 高效投入), 演化趋势如图1(e)所示。

5 激励机制下的演化博弈分析

由于现有社会经济水平和技术方法的限制, 当图书馆和技术研发企业的收益增率满足$\frac{{{C}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$和$\frac{{{C}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$时, 博弈双方选择“高效投入”的收益大于其投入成本, 小于“搭便车”效应带来的收益${{\xi }_{L}}$和${{\xi }_{E}}$, 此时博弈双方存在“搭便车”的动机, 都没有信息安全管理的投入意愿, 导致互相推脱, 图书馆的信息安全管理水平和效率难以提高。

为推动图书馆信息安全管理水平的提高与完善, 保障数字资源和用户数据的安全性, 提高图书馆的信息服务声誉, 促使技术研发企业加大信息安全投入, 扩大市场份额, 需要第三方机构采取和实施一定的激励机制, 如政府部门和文化管理机构给予图书馆一定的财政资助和补贴, 税务部门给予技术研发企业一定的减税、免税优惠。为便于模型求解, 定义激励机制如下[28]: 若博弈双方中有一方选择“高效投入”, 另一方选择“低效投入”, 则选择“高效投入”的一方将受到第三方的奖励, 奖励措施可以表现为对“高效投入”的补偿和对“低效投入”的罚金。在激励机制的作用下, 图书馆和技术研发企业的演化稳定策略会发生变化, 定义激励机制作用下的补偿(罚金)为K, 博弈双方的支付矩阵如表4所示。

表4   激励机制下的支付矩阵

   

LE
高效投入低效投入
高效投入(1+a1)PL-CL, (1+b1)PE-CE(1+a0)PL-CL+K, ξE-K
低效投入ξL-K, (1+b0)PE-CE+KPL-K, PE-K

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根据支付矩阵的收益参数, 可以得到激励机制作用下的复制动态方程如公式(10)所示。

$\left\{ \begin{align} & \frac{dx}{dt}=x(1-x)\{{{a}_{0}}{{P}_{L}}-{{C}_{L}}-[{{\xi }_{L}}-({{a}_{1}}-{{a}_{0}}+1){{P}_{L}}]y+K\} \\ & \frac{dy}{dt}=y(1-y)\{{{b}_{0}}{{P}_{E}}-{{C}_{E}}-[{{\xi }_{E}}-({{b}_{1}}-{{b}_{0}}+1){{P}_{E}}]x+K\} \\ \end{align} \right. $

(10)

令$(\frac{dx}{dt},\frac{dy}{dt})=(0,0)$, 可得该系统的5个均衡点为(0, 0)、(0, 1)、(1, 0)、(1, 1)、(A’, B’)。(A’, B’)的取值为$(\frac{{{b}_{0}}{{P}_{E}}-{{C}_{E}}+K}{{{\xi }_{E}}-({{b}_{1}}-{{b}_{0}}+1){{P}_{E}}},\frac{{{a}_{0}}{{P}_{L}}-{{C}_{L}}+K}{{{\xi }_{L}}-({{a}_{1}}-{{a}_{0}}+1){{P}_{L}}})$。

计算5个均衡点(0, 0)、(0, 1)、(1, 0)、(1, 1)、(A’, B’)的具体取值, 如表5所示。显然, 在均衡点(A’, B’)处有${{a}_{11}}+{{a}_{22}}=0$, 不满足稳定条件, 因此均衡点(A’, B’)不是演化稳定策略。

表5   激励机制下局部均衡点的参数取值

   

均衡点a11a12a21a22
(0, 0)a0PL-CL+K00b0PE-CE+K
(0, 1)a1PL-CL-ξL+PL+K00-(b0PE-CE+K)
(1, 0)-(a1PL-CL+K)00b1PE-CE-ξE+PE+K
(1, 1)-(a1PL-CL-ξL+PL+K)00-(b1PE-CE-ξE+PE+K)
(A’, B’)0a12
(A', B')
a21
(A', B')
0

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建立第三方激励机制的目的是为了促使博弈双方都选择“高效投入”的策略, 避免“搭便车”效应的形成, 因此均衡点(1, 1)应该是演化模型的唯一稳定策略。根据雅克比矩阵的稳定条件, 需要满足公式(11)。

$\begin{align} & -({{a}_{1}}{{P}_{L}}-{{C}_{L}}-{{\xi }_{L}}+{{P}_{L}}+K)<0 \\ & -({{b}_{1}}{{P}_{E}}-{{C}_{E}}-{{\xi }_{E}}+{{P}_{E}}+K)<0 \\ \end{align}$ (11)

因此, 参数K需要满足公式(12)。

$K>\max \{{{\xi }_{L}}-[({{a}_{1}}+1){{P}_{L}}-{{C}_{L}}],{{\xi }_{E}}-[({{b}_{1}}+1){{P}_{E}}-{{C}_{E}}]\}$ (12)

可知, 若参数K大于“搭便车”的收益与博弈双方共同选择“高效投入”的收益之差, 则博弈双方趋向于采取(高效投入, 高效投入)策略。因此, 第三方监管机构可以通过构建激励机制, 对选择“高效投入”的主体加以补偿, 避免“搭便车”效应的形成, 从而促进图书馆信息安全管理水平的提高。

6 仿真分析

为了更直观展示博弈双方在图书馆信息安全管理中投入意愿的演化过程, 验证构建的模型是否正确, 本文运用Matlab对不同的模型参数进行数值仿真, 分析博弈双方在演化过程中的稳定策略。

6.1 数值算例

定义博弈双方选择“低效投入”的收益为PL=6万元, PE=5万元; 博弈双方选择“高效投入”的成本CL= 3万元, CE=2万元; “搭便车”获得收益ξL=10万元, ξE= 8万元。根据上文分析, 博弈双方演化策略变化(投入收益增率)的区间临界点如下。

$\frac{{{C}_{L}}}{{{P}_{L}}}=0.5$, $\frac{{{C}_{E}}}{{{P}_{E}}}=0.4$, $\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}=1.17$,$\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}=1$

因此, 对不同演化稳定策略条件下的投入收益增率赋值, 如表6所示。

表6   投入收益增率取值

   

a0a1b0b1演化稳定策略
0.250.450.250.45(低效投入, 低效投入)
0.250.450.50.7(低效投入, 高效投入)
0.60.80.250.45(高效投入, 低效投入)
0.60.80.50.7搭便车
1.21.41.11.3(高效投入, 高效投入)

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6.2 无激励机制的仿真结果

无激励机制的仿真结果如图2所示。

图2   演化稳定策略的仿真结果

   

(1) 演化稳定策略1: 当博弈双方信息安全的投入收益增率a0=0.25, a1=0.45, b0=0.5, b1=0.7时, 满足:

$0<{{a}_{0}}<\frac{{{C}_{L}}}{{{P}_{L}}}$AND${{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$AND $0<{{b}_{0}}<\frac{{{C}_{E}}}{{{P}_{E}}}$ AND ${{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$

此时, “高效投入”给博弈双方带来的收益较小, 因此图书馆和技术研发企业在演化博弈过程中选择“低效投入”策略的比例不断增大, 最终演化稳定点为(0, 0), 演化稳定策略为(低效投入, 低效投入), 仿真结果如图2(a)所示。

(2) 演化稳定策略2: 当博弈双方信息安全的投入收益增率a0=0.25, a1=0.45, b0=0.5, b1=0.7时, 满足:

$0<{{a}_{0}}<\frac{{{C}_{L}}}{{{P}_{L}}}$ AND ${{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$ AND $\frac{{{C}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$

此时, 图书馆“高效投入”的收益仍然较小, 选择“低效投入”。技术研发企业“高效投入”的收益大于其投入成本, 但无法“搭便车”获取额外收益。因此, 演化的稳定点为(0, 1), 演化稳定策略为(低效投入, 高效投入), 仿真结果如图2(b)所示。

(3) 演化稳定策略3: 当博弈双方信息安全的投入收益增率a0=0.6, a1=0.8, b0=0.25, b1=0.45时, 满足:

$\frac{{{C}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$ AND $0<{{b}_{0}}<\frac{{{C}_{E}}}{{{P}_{E}}}$ AND ${{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$

同理, 此时图书馆“高效投入”的收益大于其投入成本, 但无法“搭便车”获取额外收益。因此, 演化的稳定点为(1, 0), 演化稳定策略为(高效投入, 低效投入), 仿真结果如图2(c)所示。

(4) 演化稳定策略4: 当博弈双方信息安全的投入收益增率a0=0.6, a1=0.8, b0=0.5, b1=0.7时, 满足:

$\frac{{{C}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}<\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}$ AND

$\frac{{{C}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}<\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}$

此时, 图书馆和技术研发企业选择“高效投入”的收益大于其投入成本, 但小于“搭便车”的收益, 最终演化的稳定点不唯一, 跟博弈双方的初始状态有关。演化稳定策略可能为(低效投入, 高效投入)或(高效投入, 低效投入), 仿真结果如图2(d)所示。

(5) 演化稳定策略5: 当博弈双方信息安全的投入收益增率a0=1.2, a1=1.4, b0=1.1, b1=1.3时, 满足:

$\frac{{{\xi }_{L}}+{{C}_{L}}-{{P}_{L}}}{{{P}_{L}}}<{{a}_{0}}<{{a}_{1}}$ AND $\frac{{{\xi }_{E}}+{{C}_{E}}-{{P}_{E}}}{{{P}_{E}}}<{{b}_{0}}<{{b}_{1}}$

此时, “高效投入”给博弈双方带来的收益大于其投入成本, 也大于“搭便车”所获收益。因此图书馆和技术研发企业在演化博弈过程中选择“高效投入”策略的比例不断增大, 最终演化稳定点为(1, 1), 演化稳 定策略为(高效投入, 高效投入), 仿真结果如图2(e) 所示。

6.3 激励机制作用下的仿真结果

为了避免形成“搭便车”效应, 需要引入第三方激励机制, 使图书馆和技术研发企业的演化稳定策略为(高效投入, 高效投入)。根据上文分析, 激励参数K需要满足:

$K>\max \{{{\xi }_{L}}-[({{a}_{1}}+1){{P}_{L}}-{{C}_{L}}],{{\xi }_{E}}-[({{b}_{1}}+1){{P}_{E}}-{{C}_{E}}]\}$

假设模型参数的取值满足“搭便车”效应形成的条件, 此时$K>\{2.2,1.5\}$, 取K=2.5, 仿真结果如图3所示。在第三方激励机制的作用下, 图书馆和技术研发企业的“搭便车”行为无法获益, 促使博弈双方选择“高效投入”策略, 从而提高图书馆信息安全管理的水平和效率。

图3   激励机制作用下演化稳定策略的仿真结果

   

7 结 语

本文从收益和成本的经济学角度出发, 将图书馆和技术研发企业视为参与主体, 尝试运用演化博弈理论分析图书馆信息安全管理的投入意愿。研究结果表明: 博弈双方关于信息安全管理的投入策略选择与其投入成本、收益增率以及“搭便车”收益密切相关, 当上述参数发生变化时, 会出现多种演化稳定策略: (低效投入, 低效投入)、(低效投入, 高效投入)、(高效投入、低效投入)、(高效投入、高效投入)以及“搭便车”行为。因此, 根据上述研究结论, 对图书馆的信息安全管理提出以下建议和对策:

(1) 提高最低投入收益增率。当信息安全管理的投入收益增率较小时, 博弈双方选择“高效投入”的收益小于成本, 或者小于“搭便车”所获收益。因此, 激励参与主体信息安全投入的最根本途径是提高信息安全管理的投入收益增率, 具体措施包括:

①加强信息安全管理和技术创新。政府部门和科研机构应实施科研计划或专项基金, 支持图书馆进行设备购买、系统更新和人员培训, 支持技术研发企业进行产品研发和市场拓展;

②提升信息安全意识。通过举办公益讲座或培训, 加强信息安全教育, 传递信息安全态度, 提高公众的信息安全意识;

③提供差异化信息服务。公共基本服务以免费或低价的形式提供给用户, 安全性更高的增值服务以较高的价格提供给用户。通过差异化服务, 图书馆和技术研发企业可以在收益和成本之间取得平衡。

(2) 降低信息安全管理的投入成本。根据文中模型分析, 图书馆与技术研发企业的信息安全投入成本负向影响投入意愿。若投入成本过高, 则博弈主体倾向于选择“低效投入”。因此, 有效的控制成本在保持投入收益增率不变的条件下, 可以降低博弈双方的投机和“搭便车”概率, 促使博弈双方选择“高效投入”。为此, 应建立总体规划的图书馆信息安全管理体系, 对相关工作进行统筹规划, 协调多部门合作, 打破组织壁垒, 实现资源共享。

(3) 加强第三方激励和问责。为了促使图书馆和技术研发企业的演化稳定策略向“高效投入”的方向演化, 需要提高其收益, 同时降低信息安全管理的投入成本, 但在目前的经济水平和技术条件下, 短期内实现收益和成本的突破具有较大难度, 需要借助外部力量, 即需要政府部门和文化管理机构给予图书馆一定的财政资助和补贴, 需要税务部门给予技术研发企业一定的减税、免税优惠。与此同时, 建立溯源和问责机制, 强化第三方的监管力度, 促使演化向“高效投入”的路径移动。

(4) 提高信息安全管理和信息服务的透明度。图书馆信息安全管理投入意愿的不足很大程度上来自管理和服务过程中的不透明性, 以及信息不对称性带来的不信任感。因此, 提高信任度和信息安全投入意愿的有效举措是信息安全管理模式和过程透明化, 保障不同主体参与和监督信息安全管理工作的权利。

(5) 制定和完善信息安全政策和法律。相关政府机构需要制定和完善相关法律法规, 建立健全的信息安全管理和信息服务体系, 推动信息安全管理的规范化和标准化, 形成信息安全投入的长效机制。

尝试设计非线性收益函数, 并分析其他因素(如用户意愿、广告效应)对投入意愿的影响是今后进一步研究的内容。

作者贡献声明

朱光: 构建模型, 起草论文;

丰米宁: 修改论文, 处理数据;

张薇薇: 论文修改。

利益冲突声明

所有作者声明不存在利益冲突关系。

支撑数据

支撑数据见期刊网络版http://www.infotech.ac.cn。

[1] 朱光. 演化博弈. txt. 数值仿真的Matlab代码.

[2] 朱光, 丰米宁. 仿真参数取值. docx. 仿真实验数据.


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https://doi.org/10.12005/orms.2015.0205      URL      [本文引用: 1]      摘要

考虑信息系统安全相互依赖情形下最优化信息系统连续时间安全投资水平是一个值得研究的问题。首先讨论了非合作博弈下信息系统安全投资的最优策略选择,在此基础上讨论了安全投资效率参数、黑客学习能力、传染风险对信息系统脆弱性及信息系统安全投资率的影响。其次,在推导出两企业在合作博弈情形下最优策略选择的基础上,对比两种情形下的博弈均衡结果,得出合作博弈下的投资水平高于非合作博弈下的投资水平。原因是两个企业的相互依赖关系隐含着企业投资的负外部性,从而导致企业投资不足。最后,构建一种双边支付激励机制消除企业投资不足问题,从而使企业达到合作博弈下的最优投资水平,提高两个企业的收益。
[19] Deng X, Han D, Dezert J, et al.

Evidence Combination from an Evolutionary Game Theory Perspective

[J]. IEEE Transactions on Cybernetics, 2016, 46(9): 2070-2082.

https://doi.org/10.1109/TCYB.2015.2462352      URL      PMID: 26285231      [本文引用: 2]      摘要

Dempster-Shafer evidence theory is a primary methodology for multisource information fusion because it is good at dealing with uncertain information. This theory provides a Dempster's rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multievidence system. Within the proposed ECR, we develop a Jaccard matrix game to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solution's stability and convergence, have been mathematically proved as well.
[20] Zhao R, Neighbour G, Han J, et al.

Using Game Theory to Describe Strategy Selection for Environmental Risk and Carbon Emissions Reduction in the Green Supply Chain

[J]. Journal of Loss Prevention in the Process Industries, 2012, 25(6): 927-936.

https://doi.org/10.1016/j.jlp.2012.05.004      URL      [本文引用: 1]      摘要

This paper provides an approach in the context of green supply chain management, using game theory to analyze the strategies selected by manufacturers to reduce life cycle environmental risk of materials and carbon emissions. Through the application of the ‘tolerability of risk’ concept, a basis for determining the extent of environmental risk and carbon emissions reduction has been established. Currently, scant attention is given to holistic supervision of the supply chain with respect to carbon emissions by governments, and thus the starting hypothesis here is that the default strategy that manufacturers will adopt is only to reduce carbon emissions, and thereby environmental risk, in so far as this is compatible with the aim of increasing revenue. Moreover, we further hypothesize that, once necessary governmental policy has been established in the supply chain management, the strategic choices of the manufacturers would be influenced by government penalties or incentives. A case example is provided to demonstrate the insight that indicates the application of game theory. The limitations of the game model and analysis are discussed, laying a foundation for further work.
[21] Demirezen E M, Kumar S, Sen A.

Sustainability of Healthcare Information Exchanges: A Game-Theoretic Approach

[J]. Information Systems Research, 2016, 27(2): 240-258.

https://doi.org/10.1287/isre.2016.0626      URL      [本文引用: 1]      摘要

Based on our interactions with the key personnel of three different healthcare information exchange (HIE) providers in Texas, we develop models to study the sustainability of HIEs and participation levels in these networks. We first examine how heterogeneity among healthcare practitioners (HPs) (in terms of their expected benefit from the HIE membership) affects participation of HPs in HIEs. We find that, under certain conditions, low-gain HPs choose not to join HIEs. Hence, we explore several measures that can encourage more participation in these networks and find that it might be beneficial to (i) establish a second HIE in the region, (ii) propose more value to the low-gain HPs, or (iii) offer or incentivize value-added services. We present several other interesting and useful results that are somewhat counterintuitive. For example, increasing the highest benefit the HPs can get from the HIE might decrease the number of HPs that want to join the HIE. Furthermore, since the amount of funds from the government and the other agencies often changes (and will eventually cease), we analyze how the changes in the benefit HPs obtain from the HIE affect (i) participation in the network, (ii) the HIE subscription fee and the fee for value-added service, (iii) the number of HPs that request value-added service, and (iv) the net values of the HIE provider and HPs. We also provide guidelines for policy makers and HIE providers that may help them improve the sustainability of HIEs and increase the participation levels in these networks.
[22] Gao X, Zhong W.

A Differential Game Approach to Security Investment and Information Sharing in a Competitive Environment

[J]. IIE Transactions, 2016, 48(6): 511-526.

https://doi.org/10.1080/0740817X.2015.1125044      URL      [本文引用: 1]      摘要

Information security economics, an emerging and thriving research topic, attempts to address the problems of distorted incentives for stakeholders in an Internet environment, including firms, hackers, the public sector, and other participants, using economic approaches. To alleviate consumer anxiety about the loss of sensitive information, and to further increase consumer demand, firms usually integrate their information security investment strategies to capture market share from competitors and their security information sharing strategies to increase consumer demand across all member firms in industry-based information sharing centers. Using differential game theory, this article investigates dynamic strategies for security investment and information sharing for two competing firms under targeted attacks, in which both firms can influence the value of their information assets through the endogenous determination of pricing rates. We analytically and numerically examine how both security investment rates and information sharing rates are affected by several key parameters in a non-cooperative scenario, including the efficiency of security investment rates, sensitivity parameters for pricing rates, coefficients of consumer demand losses, and the density of targeted attacks. Our results reveal that, confronted with a higher coefficient of consumer demand loss and a higher density of targeted attacks, both firms are reluctant to aggressively defend against hackers and would rather decrease the negative effect of hacker attacks by lowering their pricing rates. Also, we derive feedback equilibrium solutions for the situation where both firms cooperate in security investment, information sharing, or both. It is revealed that although a higher hacker attack density always decreases a firm's integral profits, both firms are not always willing to cooperate in security investment and information sharing. Specifically, the superior firm benefits most when both firms fully cooperate and benefits the least when they behave fully non-cooperatively. However, the inferior firm enjoys the highest integral profit when both firms only cooperate in information sharing and the lowest integral profit in the completely cooperative situation.
[23] Du S, Li X, Du J, et al.

An Attack-and-Defense Game for Security Assessment in Vehicular Ad Hoc Networks

[J]. Peer- to-Peer Networking and Applications, 2014, 7(3): 215-228.

https://doi.org/10.1007/s12083-012-0127-9      URL      [本文引用: 1]      摘要

Recently, there is an increasing interest in Security and Privacy issues in Vehicular ad hoc networks (or VANETs). However, the existing security solutions mainly focus on the preventive solutions while lack a comprehensive security analysis. The existing risk analysis solutions may not work well to evaluate the security threats in vehicular networks since they fail to consider the attack and defense costs and gains, and thus cannot appropriately model the mutual interaction between the attacker and defender. In this study, we consider both of the rational attacker and defender who decide whether to launch an attack or adopt a countermeasure based on its adversary’s strategy to maximize its own attack and defense benefits. To achieve this goal, we firstly adopt the attack-defense tree to model the attacker’s potential attack strategies and the defender’s corresponding countermeasures. To take the attack and defense costs into consideration, we introduce Return On Attack and Return on Investment to represent the potential gain from launching an attack or adopting a countermeasure in vehicular networks. We further investigate the potential strategies of the defender and the attacker by modeling it as an attack-defense game. We then give a detailed analysis on its Nash Equilibrium. The rationality of the proposed game-theoretical model is well illustrated and demonstrated by extensive analysis in a detailed case study.
[24] Hausken K, Zhuang J.

Governments’ and Terrorists’ Defense and Attack in a T-period Game

[J]. Decision Analysis, 2011, 8(1): 46-70.

https://doi.org/10.1287/deca.1100.0194      URL      [本文引用: 1]     

[25] Guo S X.

Environmental Options of Local Governments for Regional Air Pollution Joint Control: Application of Evolutionary Game Theory

[J]. Economic and Political Studies, 2016, 4(3):238-257.

https://doi.org/10.1080/20954816.2016.1218691      URL      [本文引用: 1]      摘要

Abstract Apanage management is currently the main method used to control air pollution in China, but it has proved to be inefficient for controlling transboundary air pollution. As a result, China’s central government is demanding joint control of regional air pollution. From the perspective of cooperation benefits, we adopt the evolutionary game theory (EGT) to analyse evolutionary trends of regional authorities’ behaviours and their stable strategy in the campaign for joint control of regional air pollution. A case study, the intergovernmental cooperation management for ‘APEC Blue’, is taken to illustrate the intergovernmental game. The result shows that an evolutionarily stable strategy (ESS) of ‘joint control’ for local governments depends on individual region’s benefits and collaboration revenues. Local governments should be encouraged in collaborating with their neighbouring governments, because a certain amount of transaction costs will not undermine their cooperation. With regards to the case study, joint control through executive orders is unpractical in the Beijing–Tianjin–Hebei region. ‘APEC Blue’ can only be temporary and the failure of such collaboration for long-term regional air pollution control is inevitable because of its high control costs, economic loss, transaction costs and low common profits.
[26] Tian Y, Govindan K, Zhu Q.

A System Dynamics Model Based on Evolutionary Game Theory for Green Supply Chain Management Diffusion among Chinese Manufacturers

[J]. Journal of Cleaner Production, 2014, 80(10): 96-105.

https://doi.org/10.1016/j.jclepro.2014.05.076      URL      [本文引用: 1]      摘要

In this study, a system dynamics (SD) model is developed to guide the subsidy policies to promote the diffusion of green supply chain management (GSCM) in China. The relationships of stakeholders such as government, enterprises and consumers are analyzed through evolutionary game theory. Finally, the GSCM diffusion process is simulated by the model with a case study on Chinese automotive manufacturing industry. The results show that the subsidies for manufacturers are better than that for consumers to promote GSCM diffusion, and the environmental awareness is another influential key factor.
[27] Friedman D.

On Economic Applications of Evolutionary Game Theory

[J]. Journal of Evolutionary Economics, 1998, 8(1): 15-43.

https://doi.org/10.1007/s001910050054      URL      [本文引用: 1]     

[28] Park J S, Kwiat K A, Kamhoua C A, et al.

Trusted Online Social Network (OSN) Services with Optimal Data Management

[J]. Computers & Security, 2014, 42(5): 116-136.

https://doi.org/10.1016/j.cose.2014.02.004      URL      [本文引用: 1]      摘要

Online Social Network (OSN) services have rapidly grown into a wide network and offer users a variety of benefits. However, they also bring new threats and privacy issues to the community. Unfortunately, there are attackers that attempt to expose OSN users' private information or conceal the information that the user desire to share with other users. Therefore, in this research we develop a framework that can provide trusted data management in OSN services. We first define the data types in OSN services and the states of shared data with respect to Optimal, Under-shared, Over-shared, and Hybrid states. We also identify the facilitating, detracting, and preventive parameters that are responsible for the state transition of the data. In a reliable OSN service, we address that a user should be able to set up his or her desired level of information sharing with a certain group of other users. However, it is not always clear to the ordinary users how to determine how much information they should reveal to others. In order to support such a decision, we propose an approach for helping OSN users to determine their optimum levels of information sharing, taking into consideration the payoffs (potential Reward or Cost) based on the Markov decision process (MDP). As an extension of the MDP-based approach, we also introduce a game theoretic approach, considering the interactions of OSN users and attackers with conflicting interests whose decisions affect each other's. Finally, after developing the framework for the optimal data sharing on OSNs, we conduct several experiments with attack simulation based on the proposed ideas and discuss the results. Our proposed approach has the capability to allow a large amount of variables to be altered to suit particular setups that an organization might have.
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