This article uses the utility functions from Richardson arms rivalry (R-AR) models to help determine the equilibrium outcomes of 2 × 2 game-theory arms rivalry (GT-AR) models. Three different formulations of a R-AR, one general and two specific, are employed. Four different formulations of a GT-AR, a PD arms rivalry (PD-AR), a Chicken arms rivalry (Chicken-AR), a Deadlock arms rivalry (Deadlock-AR), and a Stag Hunt arms rivalry (Stag Hunt-AR), are also used. I first establish the most general possible restrictions on Richardson-type utility functions that determine the four common 2 × 2 arms rivalry games. I then establish two counterintuitive results: One of the specific formulations of a R-AR may help imply the equilibrium outcomes of a PD- or Deadlock-AR but is inconsistent with the equilibrium outcomes of a Chicken- or Stag Hunt-AR; it is impossible for either specific formulation of a R-AR to ever yield the equilibrium outcome of a Stag Hunt-AR.
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