By Yoram Weiss, Gideon Fishelson

ISBN-10: 0312027974

ISBN-13: 9780312027971

ISBN-10: 1349106887

ISBN-13: 9781349106882

ISBN-10: 1349106909

ISBN-13: 9781349106905

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**Example text**

We are now in a position to write the market values of the firms and the workers. 3) r and qUit) = qUlt,f,g) is the probability that a worker of type t has i successes (this probability is calculated, given the players strategies, according to Bayes' rule). The term V f [(t,j),x,g,f], the expected profit for the firm from meeting a worker of type (t,j), has no relevance for the firm's decision problem, because the firm cannot observe j. 4) An equilibrium in the market can now be refined as follows: Definition: that A market equilibrium is a set of strategies {g* ,/*} such (a) For every gEG, and for every t, vf [t,x,g* ,/*] ~ vf [t,x,g,/*] (b) For every (t,j) and for every EF, VO [(t,j),z,g* ,/*] ~ [(t,j),z,g* ,f) Vo Note that q and the formation of beliefs are not introduced explicitly into the definition of the equilibrium because, in any particular game, the firm cannot observe any deviation of the worker from his equilibrium strategies in previous games.

Also, the other firms will not be able to observe him deviating in this game. Therefore, we are able to calculate q according to Bayes' rule in any situation. 40 Search Unemployment: Theory and Measurement It should be emphasized, however, that q depends on the solution concept for the bargaining problem also. As is shown later, the solution for the bargaining problem may admit some probability of separation (for some types of workers), as part of the revealing mechanism that is used. Therefore, whenever we specify equilibrium strategies, we have to specify a q which is evaluated according to Bayes' rule, taking into account the probability of separation that is given by the solution for the bargaining problem.

It is easy to see that our example satisfies this property. In addition, let us define the following: 26 Search Unemployment: Theory and Measurement Vf = the expected profits of a firm from being in the market, before meeting a partner vik) = the expected utility of a firm that has a partner with k checks vo(k) = the expected utility of a worker of type k from 'search' () = the discount factor (common to all workers and firms), 0 < 6 < 1. The discounted market values, 6v o(k) and 6Vf represent the alternative values that each party can obtain upon a separation.

### Advances in the Theory and Measurement of Unemployment by Yoram Weiss, Gideon Fishelson

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