On stability of Bertrand-Nash equilibrium in a simple model of the labour market

We examine a Bertrand-Edgeworth model of competition in a labour market where the workers simultaneously set wages disregarding any influence their current decision may have on opponents' future decisions. The iterated best response process is shown to converge in finite time to a Bertrand-Nash solution, where wages are set at the market-clearing level. This convergence result is also shown to hold when the assumption of static expectations is replaced by milder restrictions on beliefs about opponents'' wages.