On-the-job search is something we all do from time to time. Indeed, a significant percentage of job changes made by workers involves no interim unemployment. The object of the study is to develop and analyze a labor market model where unemployed workers and firms bargain over the wage paid if employment is accepted. Any employed worker can choose to search for another job but only at a cost. It will be shown that in such an environment the bargaining set is not convex. Nevertheless, utilizing a strategic bargaining game we show there is a unique bargaining outcome which may involve a lottery. The resulting market equilibrium exists and if the cost of search is low enough the resulting equilibrium is where some employees search on-the-job even in the case where both workers and firms are homogeneous.
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