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Matching as a Stochastic Process

Friedel Bolle and Philipp E. Otto

Abstract

Results of multi-party bargaining are usually described by concepts from cooperative game theory, in particular by the core. In one-on-one matching, core allocations are stable in the sense that no pair of unmatched or otherwise matched players can improve their incomes by forming a match. Because of incomplete information and bounded rationality, it is difficult to adopt a core allocation immediately. Theoretical investigations cope with the problem of whether core allocations can be adopted in a stochastic process with repeated re-matching. In this paper, we investigate sequences of matching with data from an experimental 2×2 labor market with wage negotiations. This market has seven possible matching structures (states) and is additionally characterized by the negotiated wages and profits. First, we describe the stochastic process of transitions from one state to another including the average transition times. Second, we identify different influences on the process parameters as, for example, the difference of incomes in a match. Third, allocations in the core should be completely durable or at least more durable than comparable out-of-core allocations, but they are not. Final bargaining results (induced by a time limit) appear as snapshots of a stochastic process without absorbing states and with only weak systematic influences.

JEL: C78; C91; D40; D82; J41

Acknowledgement

We thank Wolfgang Schmid for helpful advice concerning methodological issues. Furthermore, two reviewers and the editor of this journal made valuable proposals for improving the paper. The project support by the German Science Foundation (DFG: BO 747/11) is gratefully acknowledged.

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Supplemental Material

The online version of this article (DOI: 10.1515/jbnst-2015-1017) offers supplementary material, available to authorized users.


Received: 2015-1-6
Revised: 2015-8-3
Accepted: 2015-10-9
Published Online: 2016-3-12
Published in Print: 2016-5-1

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