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Job matching and coalition formation with utility or disutility of co-workers. (English) Zbl 1016.91070
Under the assumption that co-workers may generate utility or disutility in the workplace the model of the job matching market introduced in [A. S. Kelso jun. and V. P. Crawford, Econometrica 50, 1483-1504 (1982; Zbl 0503.90019)] is investigated. It is shown that this assumption may affect the emptyness of the core.
Suggested model of a labor market is $${\mathcal M}= (F, W, f, u)$$, where $$F= \{1, \dots, n \}$$ is the set of firms, $$W= \{1, \dots, m \}$$ is the set of workers, $$f =(f_{1}, \dots ,f_{n})$$ ($$f_{i}$$ is the production function for the firm $$i \in F$$) and $$u= \{ u_{1}, \dots, u_{m} \}$$ ($$u_{j}(S_{i},i)$$ is the utility function for the worker $$j$$ if he is hired by the firm $$i$$ and his co-worker in the firm $$i$$ is $$S_{i}$$). The profit function $${\pi}_{i} : 2^{W} \times \mathbb{R}^{nm}_{+} \to \mathbb{R}$$ for the firm $$i$$ is determined by $${\pi}_{i}(S_{i},p) =f_{i}(S_{i})- \sum_{j \in S_{i}} p_{ij}$$ ($$(p_{i1}, \dots, p_{im})$$ is the wage offers to workers by the firm $$i$$) and the surplus function $$v_{j}: W_{j} \times \mathbb{R}^{nm}_{+} \to \mathbb{R}$$ ($$W_{j}= \{ S\subset W \mid j \in S \}$$) for the worker $$j$$ if he is hired by the firm $$i$$ is defined by $$v_{j}(S_{i}, p)= p_{ij}+ u_{j}(S_{i}, i)$$. The Marshallian aggregate surplus in the labor market $$\mathcal M$$ is determined by $V= \max_{S_{0},S_{1}, \dots, S_{n} \in {\mathcal P}(W)} \sum_{i \in F} (f_{i}(S_{i})+ \sum_{j \in S_{j}} u_{j}(S_{i}, i)),$ where $$S_{0}$$ is the set of all unemployed workers. The coalition form game for the labor market $$\mathcal M$$ is determined by $w(T)= \max_{ {\mathcal S} \in {\mathcal P}(T)} \sum_{i \in T \cap F} (f_{i}(S_{i})+ \sum_{j \in S_{j}} u_{j}(S_{i}, i)),$ where $$T \subset F \cup W$$.
Some sufficient conditions for a nonempty core are established, competitive equilibrium and the tax/subsidy system are studied. The example of the labor market with an empty core for the case when money are not available in the market is designed.

##### MSC:
 91B40 Labor market, contracts (MSC2010) 91A12 Cooperative games
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##### References:
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