Does bargaining matter in the small firm's matching model?

In this article, we use a stylized model of the labor market to investigate the effects of three alternative and well-known bargaining solutions. We apply the Nash, the Egalitarian and the Kalai-Smorodinsky bargaining solutions in the small firm's matching model of unemployment. To the best of our knowledge, this is the first attempt to implement and systematically compare these solutions in search-matching economies. Our results are twofold. First from the theoretical and methodological viewpoint, we extend a somewhat flexible search-matching economy to alternative bargaining solutions. In particular, we prove that the Egalitarian and the Kalai-Smorodinsky solutions are easily implementable within search-matching economies. Second, our results show that even though the traditional results of bargaining theory apply in this context, they are generally qualitatively different from the standard results, and the differences are quantitatively weaker than expected. This is of particular relevance in comparison with the results established in the earlier literature.