Information Structure of Defection Decisions in a Colonel Blotto Model of Deterrence
Abstract: In strategic interactions, deterrence is an outcome where one party incentivizes the other party to not participate. This concept can be applied to Colonel Blotto games between two generals where troops can be deterred from following orders by the actions of the opposing general. In this setting, deterrence depends not only on how generals allocate troops, but also on the information available to troops when they decide whether to follow orders or defect. In this work, we study a two-battlefield Colonel Blotto model of deterrence under multiple information structures, ranging from decisions made with only aggregate information to decisions made after local battlefield conditions are observed. We show how different information structures alter the structure of the induced game, affect the existence of equilibria, and substantially change expected utilities. Our findings also prove that the ratio of troops available to each general combined with a capture probability threshold is enough to inform generals about what information they want their troops to have access to.