Analyzing Self-Defense Investments Under Cyber Insurance Coverage

Since cyber risks are multi-step propagated in a network,they can't be completely eliminated only through self-defense investments.Some researchers have introduced cyber insurance as an effective tool to transfer the residual risks,thus the key issue is about how much would be invested in self-defense investments when cyber insurance is offered.Besides,the interdependence of cyber risks may lead to negative externality and affects social welfare as a result.In this paper,a fully connected network is introduced to the game-theoretic model of users who make both self-defense investments and purchase cyber insurance.All the users in the network are defined as players in the game,and the optimal self-defense investments to achieve the optimal individual and social welfare are studied.For the research issue above,based on graph theory,the direct risk probability and indirect risk probability are calculated,and a more accurate game-theoretic model on user's self-defense investments is established.According to this model,the optimal self-defense investment under individually decision-making circumstance is firstly obtained,which is the pure strategy Nash equilibrium in this non-cooperative game.However,since the Nash equilibrium only guarantees the optimization of individual welfare,this paper finds that the social welfare in such case is not optimal by verifying the Pareto validity of the Nash equilibrium.Therefore,by following the Pareto improvement method,a game-theoretic model in which all users cooperate on determining their self-defense investments is established,and the optimal self-defense investment under cooperation is obtained,which is the Pareto optimal solution in the cooperative game.Finally,the Pareto optimal solution and the Nash equilibrium are compared through theoretical analysis and numerical simulation.The results show that the Pareto optimal solution is larger than the Nash equilibrium,which means users invest more in self-defense in case of cooperation than in case of non-cooperation,and the global utility of all users in the network is also improved.The result indicates that the cooperation of individuals in the network can incentivize individuals to make more self-defense investments and result in better social welfare.From the theoretical point of view,the results of this paper can be of benefit to the design of cyber insurance policy,so that individuals in the network would agree to form an alliance,and jointly make a binding agreement to protect social welfare.From the perspective of personal welfare,as this paper considers the impact of self-defense investment on individual security level and welfare under cyber insurance,the measures to solve the problem of under-investment in self-defense mechanism can be designed accordingly.From the perspective of social security level,the results raise inspirations on eliminating the influence of negative externalities through cooperation,in order to achieve the optimal social welfare and optimize the overall level of social security.