Perfect Equilibrium in a Competitive Model of Arms Accumulation

We consider a model in which two countries are involved in arms accumulation. The West is a decentralized market economy whose government uses optimal taxation to provide a public good, defense. The East is a centrally planned economy. Utility depends on consumption, leisure and defense; defense is a characteristic which is an increasing function of the difference between home and foreign weapon stocks. The cooperative outcome leads to a moratorium on investment in weapons. Two non-cooperative solutions to this differential game are also considered. The first is an open-loop Nash equilibrium solution, which presumes that countries cannot condition their investment in arms on the rival's weapon stocks. The second is a perfect Nash equilibrium solution, which presumes that countries can monitor foreign weapon stocks. The perfect equilibrium solution leads to lower levels of arms and is therefore more efficient, so that a unilateral arms treaty should allow countries to observe their rival's weapon stocks. In other words, verification leads to lower weapon stocks and higher welfare for both countries. The perfect equilibrium solution also provides a more satisfactory strategic foundation for the Richardson equations.