Does bargaining matter in the small firms 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 that has been made to implement and systematically compare these solutions in search-matching economies. Our results are twofold. First from the theoretical/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 and mathematically tractable 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 and quantitatively weaker than expected. This is of particular relevance in comparison with the results established in the earlier literature.