Efficiency-wage competition: What happens as the number of players increases?

In this paper, I explore the consequences of extending the number of firms in an efficiency-wage competition framework. In this setting, I show that the effort function shape is crucial in determining key features of the model economy. Specifically, with a concave (sigmoid) effort function, the wage and the employment levels prevailing in a symmetric Nash equilibrium are, respectively, lower (higher) and higher (lower), the higher the number of competing firms. Moreover, assuming that firms adjust their wages on the basis of lagged wage bids, the adoption of a concave (sigmoid) effort function reveals that the symmetric Nash equilibrium is unstable (stable) and the speed of divergence (convergence) is an increasing function of the number of firms. Furthermore, with a concave (sigmoid) effort function the full employment equilibrium is characterized by a monopsonistic exploitation of labour that increases (decreases) with the number of productive units required to sustain that allocation. Those findings have intriguing implications for the existence of involuntary unemployment as well as for policies aimed at increasing employment.