Fast, optimal, and dynamic electoral campaign budgeting by a generalized Colonel Blotto game

The Colonel Blotto game is a deeply studied theoretical model for competitive allocation environments including elections, advertising, and ecology. However, the original formulation of Colonel Blotto has had few practical implications due to the lack of fast algorithms to compute its optimal strategies and the limited applicability of its winner-take-all reward distribution. We demonstrate that the Colonel Blotto game can be a practical model for competitive allocation environments by implementing the multiplicative weights update algorithm from Beaglehole et al. (2023). In particular, using that this algorithm allows for arbitrary winning-rules, we study strategies for a more realistic model of political campaigning we term Electoral Colonel Blotto. Contrary to existing theory and the implemented allocation strategies from U.S. presidential elections, we find that the optimal response to Democratic and Republican strategies in the 2008 and 2020 presidential elections was to focus allocations on a subset of states and sacrifice winning probability on others. We also found that campaigners should compete for undecided voters even in states where the opponent has significantly many more decided voters.