On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets
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We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation/dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation/dropping strategies. We prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1—Example 1), nor to group manipulations (even when all quotas equal 1—Example 2).
KeywordsStable Mechanism Potential Partner Stable Matchings Preference List Truncation Strategy
We would like to thank Lars Ehlers, Jordi Massó, William Thomson, Hanzhe Zhang, an associate editor, and two anonymous referees for helpful comments on an earlier draft of the paper. We thank the seminar participants at Universidad de los Andes, Universidad del Rosario, GAMES 2012, and First Caribbean Game Theory Conference for valuable discussions. Ç. Kayı gratefully acknowledges the hospitality of Institute for Economic Analysis (CSIC) and financial support from Colciencias/CSIC (Convocatoria No: 506/2010), El Patrimonio Autónomo Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación, Francisco José de Caldas. The first draft of this paper was written while F. Klijn was visiting Universidad del Rosario. He gratefully acknowledges the hospitality of Universidad del Rosario and financial support from CSIC/Colciencias through grant 2010C00013 and the Spanish Ministry of Economy and competitiveness through Plan Nacional I+D+i (ECO2011–29847) and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075).
- Alkan A (1999) On the properties of stable many-to-many matchings under responsive preferences. In: Alkan A, Aliprantis CD, Yannelis NC (eds) Current trends in economics: theory and applications, vol 8. Studies in economic theory. Springer, BerlinGoogle Scholar
- Alkan A (2001) On preferences over subsets and the lattice structure of stable matchings. Rev Econ Des 6(1):99–111Google Scholar
- Coles P, Shorrer R (2012) Optimal truncation in matching markets. Mimeo, Harvard Business School, AllstonGoogle Scholar
- Dubins LE, Freedman DA (1981) Machiavelli and the gale-shapley algorithm. Am Math Mon 88(7): 485–494Google Scholar
- Echenique F, Oviedo J (2006) A theory of stability in many-to-many matching markets. Theor Econ 1(2):233–273Google Scholar
- Klijn F, Yazıcı A (2012) A many-to-many ‘Rural Hospital Theorem’. Barcelona Graduate School of Economics, Working Paper 567Google Scholar
- Mongell S, Roth AE (1991) Sorority rush as a two-sided matching mechanism. Am Econ Rev 81(3):441–464Google Scholar
- Romm A (2011) Mechanism-free implications of entry and capacity reduction in many-to-one stable matching. Mimeo, Harvard Business School, AllstonGoogle Scholar
- Roth AE (1991) A natural experiment in the organization of entry-level labor markets: regional markets for new physicians and surgeons in the United Kingdom. Am Econ Rev 81(3):415–440Google Scholar
- Roth AE, Sotomayor MAO (1990) Two-sided matching: a study in game-theoretic modeling and analysis. Cambridge University Press, Econometric Society Monograph Series, New YorkGoogle Scholar