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Purpose

Aims to analyse the labour market outcome when there are two unions in the industry, representing heterogeneous workers – imperfect substitutes in production.

Design/methodology/approach

Competition between union policies are viewed in terms of both employment and wage strategies. Results for substitutes and complements are inspected. Attention is given to the strategic behaviour of the unions, towards one another and/or the employer side. Cooperation is modelled using the Nash‐maximand approach.

Findings

Gathers some notes and enlargements to the standard collective bargaining problem in which unions maximise utility. Extends the framework to model union competition behaviour for jobs and/or employment that reproduces the standard market product analysis of imperfect competition. Focuses on heterogeneous labour.

Research limitations/implications

The analysis concentrates on the case of union duopoly, but can easily be enlarged to the n‐union setting – which is left for further investigation.

Originality/value

A simple analytical example with Stone‐Geary union utility functions and a linear labour demand system is forwarded.

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