By Yoram Weiss, Gideon Fishelson
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In this case, a new firm he arrives at may suspect that other firms have already found him to be 'bad'. Therefore, even if the firm likes him, it may attempt to use his weak bargaining position by offering him a low wage. This idea is modelled as follows. Workers arrive at firms and bargain over wages. Each firm does not know the true productivity of a particular worker, but it can find this out by testing the worker. Because there is some correlation among firms, if one firm finds the worker unfit to its needs, the chances that other firms may find him unfit increase.
A wage is determined according to the expected payoff of each player. The worker will get this wage if he is found to be a good match. If he is a bad match, no production and payments take place, and the parties separate. (2) A post-check contract - the firm decides whether to check the worker or not before the bargaining takes place. If it checks the worker and finds him to be a good match, they bargain over the wage (if the worker wants to). If the worker is a bad match, they separate. I describe now the solution for the bargaining game under the pre-check contract (that post-check contract is described in Section 4).
Each period a machine randomly and costlessly assigns workers to firms. Workers, therefore, have no cost of searching for open jobs, but can search only one firm per period. When a worker and a firm meet, they cannot observe the true value of the match. Instead, they both have some beliefs about the probability of a good match. In addition, the firm can costlessly check the true quality of the match. The check fully reveals whether or not the worker is a good match or not. If the firm does not want to check the worker or the worker does not want to be checked, they break off negotiation.