Cascade of coordinated behaviors in interdependent security games

How do we get collective rationality, if each person obeys individual rationality to maximize personal utility? This question has been studied extensively using theory of games. Here we consider scenarios where the individuals' behavior is the result of a strategic choice among competing alternatives. In particular, we study interdependent security game that is based on the dynamics of coordination games on networks. In the game, each agent has to select whether adopt the cost for security measure or not. An agent investing in security measure is safe against internal risk, but it still has external risk imposed by other agents who do not have invested in security measure. The external risk reduces the incentive for other agents to invest. Classical results in game theory studying this model provide a simple condition for a risk-dominant behavior to become widespread in the agent-network. The essential idea is to show how efficient coordination can emerge spontaneously at the collective level from the pair-wise interactions of adaptive agents, where strategic choices of agents often lead to inefficient outcomes. Cascade processes are progressive in the sense that once a node switches from one state B to another state A, it remains in state A in all subsequent time steps. The stochastic threshold model can introduce the rationality of agents effectively. The stochastic threshold model describes the adaptive behavior and leads to the cascade dynamics. We show that the cascade driven by the stochastic threshold model promotes collective behavior to efficient outcomes: all agents adopt the cost for security and the society is completely free from risk.