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We study games with nonlinear best response functions played on a network consisting of disjoint communities. Prior works on network games have identified conditions to guarantee the uniqueness and stability of Nash equilibria in a network without any community structure. In this paper we are interested in accomplishing the same for networks with a community structure; it turns out that these conditions are much easier to verify with certain community structures. Specifically, we consider multipartite graphs and show that the uniqueness and stability of Nash equilibria are related to matrices which are potentially much lower in dimension, on the order of the number of communities, compared to same-size networks without a multipartite structure, in which case such matrices have a dimension the size of the network. We further introduce a new notion of degree centrality to measure the importance and influence of a community in such a network. We show that this notion enables us to find new conditions for uniqueness and stability of Nash equilibria. 

Cyber insurance like other types of insurance is a method of risk transfer, where the insured pays a premium in exchange for coverage in the event of a loss. As a result of the reduced risk for the insured and the lack of information on the insurer’s side, the insured is generally inclined to lower its effort, leading to a worse state of security, a common phenomenon known as moral hazard. To mitigate moral hazard, a widely employed concept is premium discrimination, i.e., an agent/insured who exerts higher effort pays less premium. This, however, relies on the insurer’s ability to assess the effort exerted by the insured. In this paper, we study two methods of premium discrimination that rely on two different types of assessment: pre-screening and post-screening. Pre-screening occurs before the insured enters into a contract and can be done at the beginning of each contract period; the result of this process gives the insurer an estimated risk on the insured, which then determines the contract terms. The post-screening mechanism involves at least two contract periods whereby the second-period premium is increased if a loss event occurs during the first period. Prior work shows that both pre-screening and post-screening are generally effective in mitigating moral hazard and increasing the insured’s effort. The analysis in this study shows, however, that the conclusion becomes more nuanced when loss events are rare. Specifically, we show that post-screening is not effective at all with rare losses, while pre-screening can be an effective method when the agent perceives them as rarer than the insurer does; in this case pre-screening improves both the agent’s effort level and the insurer’s profit. 

We consider an InterDependent Security (IDS) game with networked agents and positive externality where each agent chooses an effort/investment level for securing itself. The agents are interdependent in that the state of security of one agent depends not only on its own investment but also on the other agents' effort/investment. Due to the positive externality, the agents under-invest in security which leads to an inefficient Nash equilibrium (NE). While much has been analyzed in the literature on the under-investment issue, in this study we take a different angle. Specifically, we consider the possibility of allowing agents to pool their resources, i.e., allowing agents to have the ability to both invest in themselves as well as in other agents. We show that the interaction of strategic and selfish agents under resource pooling (RP) improves the agents' effort/investment level as well as their utility as compared to a scenario without resource pooling. We show that the social welfare (total utility) at the NE of the game with resource pooling is higher than the maximum social welfare attainable in a game without resource pooling but by using an optimal incentive mechanism. Furthermore, we show that while voluntary participation in this latter scenario is not generally true, it is guaranteed under resource pooling.