  Foreign power interference in domestic elections is an existential threat to
societies. Manifested through myriad methods from war to words, such
interference is a timely example of strategic interaction between economic and
political agents. We model this interaction between rational game players as a
continuous-time differential game, constructing an analytical model of this
competition with a variety of payoff structures. All-or-nothing attitudes by
only one player regarding the outcome of the game lead to an arms race in which
both countries spend increasing amounts on interference and
counter-interference operations. We then confront our model with data
pertaining to the Russian interference in the 2016 United States presidential
election contest. We introduce and estimate a Bayesian structural time series
model of election polls and social media posts by Russian Twitter troll
accounts. Our analytical model, while purposefully abstract and simple,
adequately captures many temporal characteristics of the election and social
media activity. We close with a discussion of our model's shortcomings and
suggestions for future research.
