Combining Richardson's equations with canard explosion theory in a genetic algorithm to predict instabilities in the India/Pakistan arms race

Abstract

The mid-1998 troubles between India and Pakistan are used to demonstrate that a real-valued Genetic Algorithm (GA) can find workable solutions to Richardson's Theory of Arms Races. Rough ‘starter' values for the rate-constants in Richardson's equations are gleaned from International Monetary Fund statistics. The resulting GA found, first, that very small changes in percentage defence expenditure made all the difference between stability and instability; second, that although there are dangerous pockets of potential instabihty in the developing arms race, nevertheless there are large areas of stability as well; and third, that by ‘borrowing' a concept from Brans and Bar-Eli's adaptation of the Peng et al, model of canard explosions and by examining the asymptotic behaviour of the limit cycle, it is possible to predict when war is likely to erupt. Properly refined, such predictions could be used to prevent an arms race from escalating into open war.

Keywords:

• Genetic algorithms
• Canard explosions
• Limit cycles
• Arms races
• Richardson's equations

C.R. Categories::

• C.3
• F.4
• G.4
• I.6
• K.4.2