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Matching as a Stochastic Process

  • Friedel Bolle and Philipp E. Otto EMAIL logo


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


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.


Abreu, D., F. Gul (2000), Bargaining and Reputation. Econometrica 68 (1): 85–117.Search in Google Scholar

Bayer, C., K. Wälde (2011). Describing Distributions in Search and Matching Models by Fokker-Planck Equations. Gutenberg School of Management and Economics Working Paper 1110.Search in Google Scholar

Béal, S., E. Rémila, P. Solal (2012), An Optimal Bound to Access the Core in TU-Games. mpra Working Paper.Search in Google Scholar

Binmore, K., L. Samuelson, P. Young (2003), Equilibrium Selection in Bargaining Models. Games and Economic Behavior 45: 296–328Search in Google Scholar

Biró, P., M. Bomhoff, P.A. Golovach, W. Kern, D. Paulusma (2012), Solutions for the Stable Roommates Problem with Payments. 69–80 in: Graph-Theoretic Concepts in Computer Science. Berlin Heidelberg, Springer.Search in Google Scholar

Biró, P., G. Norman (2013), Analysis of Stochastic Matching Markets. International Journal of Game Theory 42 (4): 1021–1040.Search in Google Scholar

Bolle, F., P.E. Otto (2016), Role-Dependent Social Preferences. Economica (in press).Search in Google Scholar

Breitmoser, Y., F. Bolle, P.E. Otto (2012), The Core with Random Utility and Interdependent Preferences: Theory and Experimental Evidence. mpra Working Paper 42819.Search in Google Scholar

Cappelen, A.W., A.D. Hole, E.Ø. Sørensen, E. Tungodden (2007), The Pluralism of Fairness Ideals: An Experimental Approach. American Economic Review 97 (3): 818–827.Search in Google Scholar

Charness, G., M. Corominas-Bosch, G.R. Frechette (2007), Bargaining and Network Structure: An Experiment. Journal of Economic Theory 136 (1): 28–65.Search in Google Scholar

Chen, B., S. Fujishige, Z. Yang (2010), Decentralized Market Processes to Stable Job Matchings with Competitive Salaries. KIER Discussion Paper 749.Search in Google Scholar

Heuer, A., O. Rubner (2012), How Does the Past of a Soccer Match Influence Its Future? Concepts and Statistical Analysis. PLOS ONE 7 (11): e47678.Search in Google Scholar

Klaus, B., F. Payot (2013), Paths to Stability in the Assignment Problem. Cahier de Recherches Économiques University of Lausanne Working Paper 13.14.Search in Google Scholar

Koopmans, T.J., M. Beckmann (1957), Assignment Problems and the Location of Economic Activity. Econometrica 25 (1): 53–76.Search in Google Scholar

Launov, A., K. Wälde (2013). Estimating Incentive and Welfare Effects of Nonstationary Unemployment Benefits. International Economic Review 54 (4): 1159–1198.Search in Google Scholar

McKelvey, R., T. Palfrey (1998), Quantal Response Equilibria for Extensive Form Games. Experimental Economics 1: 9–41.Search in Google Scholar

Mortensen, D.T. (1988), Matching: Finding a Partner for Life or Otherwise. American Journal of Sociology 94 (Supplement: Organizations and Institutions): 215–240.Search in Google Scholar

Nave, G., A. Smith, C. Camerer (2015). Semistructured Bargaining with Private Information and Deadlines. Available at: in Google Scholar

Nax, H.H., B.S.R. Pradelski (2015), Evolutionary Dynamics and Equitable Core Selection in Assignment Games. International Journal of Game Theory 44 (4): 903–932.Search in Google Scholar

Nax, H.H., B.S.R. Pradelski, H.P. Young (2013), The Evolution of Core Stability in Decentralized Matching Markets. FEEM Working Paper 50.2013.Search in Google Scholar

Nowak, M. (1990). Stochastic Strategies in the Prisoner’s Dilemma. Theoretical Population Biology 38: 93–112.Search in Google Scholar

Ostmann, A. (1992), The Interaction of Aspiration Levels and the Social Field in Experimental Bargaining. Journal of Economic Psychology 13 (2): 233–261.Search in Google Scholar

Otto, P.E., F. Bolle (2011), Matching Markets with Price Bargaining. Experimental Economics 14: 322–348.Search in Google Scholar

Press, W.H., D.J. Freeman (2012), Iterated Prisoner’s Dilemma Contains Strategies that Dominate any Evolutionary Opponent. PNSA 109 (26): 10409–10413.Search in Google Scholar

Rubinstein, A. (1982), Perfect Equilibrium in a Bargaining Model. Econometrica 50 (1): 97–109.Search in Google Scholar

Selten, R. (1972), Equal Share Analysis of Characteristic Function Experiments. 130–165 in: H. Sauermann (Ed.), Beiträge zur experimentellen Wirtschaftsforschung (Vol. 111), Tübingen, Mohr.Search in Google Scholar

Shapley, L.S. (1953), Stochastic Games. PNSA 39 (10): 1095–1100.Search in Google Scholar

Shapley, L.S., M. Shubik (1971). The Assignment Game, I: The Core. International Journal of Game Theory 11: 111–130.Search in Google Scholar

Sandholm, W.H. (2010), Population Games and Evolutionary Dynamics. MIT Press, Cambridge.Search in Google Scholar

Tietz, R., O.J. Bartos (1982). Balancing of Aspiration Levels as Fairness Principle in Negotiations. Professur für Volkswirtschaftslehre, insbesondere Verhaltensforschung: Johann Wolfgang Goethe-Universität.Search in Google Scholar

Yang, Y.-Y. (2010), On the Accessibility of the Core. Games and Economic Behavior 69 (1): 194–199.Search in Google Scholar

Young, H.P. (1998). Conventional Contracts. Review of Economic Studies 65 (4): 773–792.Search in Google Scholar

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

©2016 by De Gruyter Mouton

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