A correspondence principle for cooperative differential equations

This paper establishes a correspondence principle in a system of cooperative differential equations. Equilibria that are locally asymptotically stable must exhibit monotone comparative statics. In a wider context, all equilibria that exhibit monotone comparative statics are locally asymptotically stable. The orbits of such systems are nondecreasing in the parameter and the adjustment dynamics after a parameter change are monotone and convergent to a unique limit. Our results can be applied to such models as adaptive play in games with strategic complementarities, stochastic fictitious play in supermodular games, and the Matsuyama [6] model of global financial market liberalization with multiple capital goods.