The process of wage determination is one of the most important institutional features of an economy. It determines the response to exogenous shocks and affects the long run perfomance as far as employment is concerned. For most western European countries the role of unions in that process is very important, regardless the size of the unions itself. It has become fashionable the explicit consideration of the unions both in theoretical and empirical macroeconomics. In this papel, a very particular issue of a unionized labour market is analyzed; We shall study an economy with several unions, and consider the different wage/employment outcomes with result from alternative strategic behaviour of those (rational) unions. The model adopts a differential game format in wich each union choses its policy instrument, taking in account the (passive) response of the employer (through the labour demand) and the existence of other union(s) operating in the same firm. The state variable is the wage level; its dynamic is driven by the instruments choosen by the union plus some exogenos factors wich determine the relative bargaining power of firm and unions
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