  Ensuring public safety in a Smart City (SC) environment is a critical and
increasingly complicated task due to the involvement of multiple agencies and
the city's expansion across cyber and social layers. In this paper, we propose
an extensive form perfect information game to model interactions and optimal
city resource allocations when a Terrorist Organization (TO) performs attacks
on multiple targets across two conceptual SC levels, a physical, and a
cyber-social. The Smart City Defense Game (SCDG) considers three players that
initially are entitled to a specific finite budget. Two SC agencies that have
to defend their physical or social territories respectively, fight against a
common enemy, the TO. Each layer consists of multiple targets and the attack
outcome depends on whether the resources allocated there by the associated
agency, exceed or not the TO's. Each player's utility is equal to the number of
successfully defended targets. The two agencies are allowed to make budget
transfers provided that it is beneficial for both. We completely characterize
the Sub-game Perfect Nash Equilibrium (SPNE) of the SCDG that consists of
strategies for optimal resource exchanges between SC agencies and accounts for
the TO's budget allocation across the physical and social targets. Also, we
present numerical and comparative results demonstrating that when the SC
players act according to the SPNE, they maximize the number of successfully
defended targets. The SCDG is shown to be a promising solution for modeling
critical resource allocations between SC parties in the face of multi-layer
simultaneous terrorist attacks.
