A time-integrated Richardson model

Richardson equations are widely studied models of simplified multi-player arms races. In this paper, we derive a novel and more theoretically-consistent formulation, which implicitly includes a mapping from observed economic data to the model variables. We define new variables which are time-integrated versions of scaled ‘defense’ expenditures, and show that they may be robustly estimated from historical data. We illustrate the model's usefulness with historical examples and a simplified risk analysis of simulated data.