The role of risk preferences in a multi-target defender-attacker resource allocation game

•We study risk preferences of both attacker and defender in a sequential game.•We study how risk preferences affect a player's behavior in equilibrium.•We compare the new model with the one does not consider risk preferences.•We find the model utility is high especially when the attacker is risk seeking.

This paper studies a sequential defender-attacker game, where the defender allocates defensive resources to multiple potential targets while considering the risk preferences of both attacker and defender. We model and obtain analytical equilibrium results for this problem and study how risk preferences affect a player's behavior in equilibrium. We find that in the strategic case, when both the attacker and the defender have some target valuation, the strategic attacker's risk preferences and target valuation affect the optimal defense allocation. In particular, when the attacker becomes more risk seeking/averse, the high valuable target to the attacker would receive more/less resources. The proposed model leads to a significantly lower expected damage than a model where the attacker is incorrectly considered risk neutral, especially when the attacker is risk seeking.