Journal of Global Optimization

, Volume 70, Issue 2, pp 413–436 | Cite as

Security investment and information sharing in the market of complementary firms: impact of complementarity degree and industry size

  • Xinbao Liu
  • Xiaofei Qian
  • Jun Pei
  • Panos M. Pardalos


We study a differential game of information security investment and information sharing in a market consisting of n complementary firms. Two game approaches, the non-cooperative game and the totally cooperative game, are employed to investigate the steady state strategy of each firm. Under certain conditions, a unique steady state can be obtained for both games. We find that the steady state security investment and information sharing level are not always less in the non-cooperative game than that in the totally cooperative game. In addition, some theoretical analyses are made on the impacts of the complementarity degree and industry size on firms’ steady state strategies for both games. Finally, some numerical experiments are conducted to give some insights related to the instantaneous profit in the steady state. It can be found that a firm will obtain more instantaneous profit in the steady state of the totally cooperative game than that of the non-cooperative game, which emphasizes the importance of coordinating strategies. The effects of the complementarity degree and industry size on the instantaneous profits in the steady state are also obtained through the numerical experiment results.


Information security investment Information sharing Differential game Complementary firms Steady state 



This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71601065, 71690235, 71690230, 71501058), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167), and the Science and Technology Project of Zhejiang Province (No. 2017C31069). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of ManagementHefei University of TechnologyHefeiPeople’s Republic of China
  2. 2.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of EducationHefeiPeople’s Republic of China

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