We consider the provision of public goods on networks of strategic agents. We study different effort outcomes of these network games, namely, the Nash equilibria, Pareto efficient effort profiles, and semi-cooperative equilibria (effort profiles resulting from interactions among coalitions of agents). We identify necessary and sufficient conditions on the structure of the network for the uniqueness of the Nash equilibrium. We show that our finding unifies (and strengthens) existing results in the literature. We also identify conditions for the existence of Nash equilibria for the subclasses of games at the two extremes of our model, namely games of strategic complements and games of strategic substitutes. We provide a graph-theoretical interpretation of agents' efforts at the Nash equilibrium, as well as the Pareto efficient outcomes and semi-cooperative equilibria, by linking an agent's decision to her centrality in the interaction network. Using this connection, we separate the effects of incoming and outgoing edges on agents' efforts and uncover an alternating effect over walks of different length in the network.
We consider a system consisting of multiple interdependent assets, and a set of defenders, each responsible for securing a subset of the assets against an attacker. The interdependencies between the assets are captured by an attack graph, where an edge from one asset to another indicates that if the former asset is compromised, an attack can be launched on the latter asset. Each edge has an associated probability of successful attack, which can be reduced via security investments by the defenders. In such scenarios, we investigate the security investments that arise under certain features of human decision-making that have been identified in behavioral economics. In particular, humans have been shown to perceive probabilities in a nonlinear manner, typically overweighting low probabilities and underweighting high probabilities. We show that suboptimal investments can arise under such weighting in certain network topologies. We also show that pure strategy Nash equilibria exist in settings with multiple (behavioral) defenders, and study the inefficiency of the equilibrium investments by behavioral defenders compared to a centralized socially optimal solution.
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