Resource Pooling for Shared Fate: Incentivizing Effort in Interdependent Security Games Through Cross-Investments

We consider an interdependent security game with networked agents where each agent chooses an effort/investment level for securing itself. The agents are interdependent in a way where the state of security of one agent depends not only on its own effort but also on that of the other agents, and each agent can benefit from other agents' security investment and effort. Since the agents are interdependent, they try to take advantage of others' security investment and effort and choose to under-invest, which leads to an inefficient Nash equilibrium (NE). While this has been analyzed extensively in the literature, in this study, we take a different angle. Specifically, we consider the possibility of allowing agents to pool their resources, i.e., 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 level as well as their utility compared to a scenario without RP. We show that the social welfare (total utility) at the NE of the game with RP is higher than the maximum social welfare attainable in a game without RP but using an optimal incentive mechanism. Furthermore, we show that while voluntary participation in the latter scenario here, is not generally true, it is guaranteed under RP.