Fairness models for multi-agent kidney exchange programmes

•We address fairness in multi-agent Kidney Exchange Programmes (mKEP) as a means to incentive collaboration between agents.•New Integer Programming models are proposed for balancing the benefits of agents in an mKEP in the long term.•The impact on the performance of the mKEP of different agents behaviours and management policies is analysed through thorough computational analysis.•To our best knowledge, this is the first time that the impact of arbitrariness in the choice of an optimal solution in an mKEP is addressed.