Abstract
We consider two-sided matching markets, and study the incentives of agents to circumvent a centralized clearing house by signing binding contracts with one another. It is well-known that if the clearing house implements a stable match and preferences are known, then no group of agents can profitably deviate in this manner.
We ask whether this property holds even when agents have incomplete information about their own preferences or the preferences of others. We find that it does not. In particular, when agents are uncertain about the preferences of others, every mechanism is susceptible to deviations by groups of agents. When, in addition, agents are uncertain about their own preferences, every mechanism is susceptible to deviations in which a single pair of agents agrees in advance to match to each other.
N. Arnosti — Work conducted at Microsoft Research.
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Notes
- 1.
In many-to-one settings, Sönmez [18] demonstrates that even in full-information environments, it may be possible for agents to profitably pre-arrange matches (a follow-up by Afacan [1] studies the welfare effects of such pre-arrangements). In order for all parties involved to strictly benefit, it must be the case that the firm hires (at least) one inferior worker in order to boost competition for their remaining spots (and thereby receive a worker who they would be otherwise unable to hire). Thus, the profitability of such an arrangement again relies on assumptions about the firm’s underlying cardinal utility function.
- 2.
Liu et al. [9] have recently grappled with this inference procedure, and defined a notion of stable matching under uncertainty. Their model differs substantially from the one considered here: it takes a matching \(\mu \) as given, and assumes that agents know the quality of their current match, but must make inferences about potential partners to whom they are not currently matched.
- 3.
We thank an anonymous reviewer for the reference.
- 4.
This result relies crucially on the fact that we’re using the notion of stochastic dominance to determine blocking pairs. If agents instead evaluate lotteries over matches by computing expected utilities, it is easy to construct examples where two agents rank each other second, and both prefer matching with certainty to the risk of getting a lower-ranked alternative from \(\phi \) (see the full version of the paper for an example).
References
Afacan, M.O.: The welfare effects of pre-arrangements in matching markets. Econ. Theor. 53(1), 139–151 (2013)
Du, S., Livne, Y.: Rigidity of transfers and unraveling in matching markets. Available at SSRN (2014)
Gudmundsson, J.: Sequences in Pairing Problems: A new approach to reconcile stability with strategy-proofness for elementary matching problems, November 2014. (Job Market Papers)
Halaburda, H.: Unravelling in two-sided matching markets and similarity of preferences. Games Econ. Behav. 69(2), 365–393 (2010)
Kagel, J.H., Roth, A.E.: The dynamics of reorganization in matching markets: a laboratory experiment motivated by a natural experiment. Q. J. Econ. 115(1), 201–235 (2000)
Li, H., Rosen, S.: Unraveling in matching markets. Am. Econ. Rev. 88(3), 371–387 (1998)
Li, H., Suen, W.: Risk sharing, sorting, and early contracting. J. Polit. Econ. 108(5), 1058–1091 (2000)
Li, H., Suen, W.: Self-fulfilling early-contracting rush. Int. Econ. Rev. 45(1), 301–324 (2004)
Liu, Q., Mailath, G.J., Postlewaite, A., Samuelson, L.: Stable matching with incomplete information. Econometrica 82(2), 541–587 (2014)
Manjunath, V.: Stability and the core of probabilistic marriage problems. Technical report, Working paper (2013)
McKinney, C.N., Niederle, M., Roth, A.E.: The collapse of a medical labor clearinghouse (and why such failures are rare). Am. Econ. Rev. 95(3), 878–889 (2005)
Niederle, M., Roth, A.E.: The gastroenterology fellowship match: how it failed and why it could succeed once again. Gastroenterology 127(2), 658–666 (2004)
Peivandi, A., Vohra, R.: On fragmented markets (2013)
Roth, A.E.: Two-sided matching with incomplete information about others’ preferences. Games Econ. Behav. 1(2), 191–209 (1989)
Roth, A.E.: 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), 415–440 (1991)
Roth, A.E., Rothblum, U.G.: Truncation strategies in matching markets in search of advice for participants. Econometrica 67(1), 21–43 (1999)
Roth, A.E., Xing, X.: Jumping the gun: Imperfections and institutions related to the timing of market transactions. Am. Econ. Rev. 84(4), 992–1044 (1994)
Sonmez, T.: Can pre-arranged matches be avoided in two-sided matching markets? J. Econ. Theor. 86(1), 148–156 (1999)
Suen, W.: A competitive theory of equilibrium and disequilibrium unravelling in two- sided matching. RAND J. Econ. 31(1), 101–120 (2000)
Yenmez, M.B.: Incentive-compatible matching mechanisms: consistency with various stability notions. Am. Econ. J. Microeconomics 5(4), 120–141 (2013)
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Arnosti, N., Immorlica, N., Lucier, B. (2015). The (Non)-Existence of Stable Mechanisms in Incomplete Information Environments. In: Markakis, E., Schäfer, G. (eds) Web and Internet Economics. WINE 2015. Lecture Notes in Computer Science(), vol 9470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48995-6_4
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