Dynamic games and growth gycles in unionised economies

In this paper we integrate the dynamic models formulated by the microeconomic theory of trade unions and the differential games approach. We demonstrate that the results of the dynamic monopoly union model, elaborated by Kidd and Oswald (1987) and Jones and McKenna (1994), can be obtained as solutions of a Stackelberg differential game between firms and unions under particular assumptions on union’s membership dynamic. We also develop a Nash differential game whose solutions imply a cycle in wage share of product and employment rate which resembles Goodwin’s (1967) cyclical growth path. This result is obtained by use of the Hopf theorem on local bifurcations, under particular hypotheses on the membership dynamics