Because a competitive labour market is supposed to provide the highest level of employment, unions and their wage bargaining power have always been seen by economists as responsible for unemployment since Pigou (1933). But to define exactly the bargaining income was not an easy task to carry out : as Edgeworth (1881) has already showed, a bilateral bargaining does not lead to a unique theoretical solution. The aim of this paper is to show how the advances in the non-cooperative games theory allowed economists to solve this multiplicity by providing strategic analyses which were consistent with the economic rationality. But many problems persist : what are the goals of unions? With which variables are they concerned? What is the proper way to make it consistent with microeconomic foundations? We show that the way economic theory answered these questions and the model which was finally chosen to represent wage bargaining, result from a normative choice (to keep the idea that unions are responsible of unemployment), inconsistent with some properties usually considered as necessary (such as Pareto efficiency).