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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.

91B40 Labor market, contracts (MSC2010)
91A12 Cooperative games
Full Text: DOI
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