Market sentiments and convergence dynamics in decentralized assignment economies
In two-sided markets with transferable utility (‘assignment games’), we study the dynamics of trade arrangements and price adjustments as agents from the two market sides stochastically match, break up, and re-match in their pursuit of better opportunities. The underlying model of individual adjustments is based on the behavioral theories of adaptive learning and aspiration adjustment. Dynamics induced by this model converge to approximately optimal and stable market outcomes, but this convergence may be (exponentially) slow. We introduce the notion of a ‘market sentiment’ that governs which of the two market sides is temporarily more or less amenable to price adjustments, and show that such a feature may significantly speed up convergence.
KeywordsAssignment games Core Evolutionary game theory Matching markets Convergence time Market psychology
Pradelski thanks Pierre Tarrès and Peyton Young for their guidance and support throughout and beyond his PhD which shaped this research. Further, this paper has benefitted from generous comments and criticism by Yakov Babichenko, Doyne Farmer, Satoru Fujishige, Olivier Gossner, Sergiu Hart, Michael Krivelevich, Jacob Leshno, Noam Nisan, Thomas Norman, Bill Sandholm, Jay Sethuraman, Eran Shmaya, Gregory Sorkin and Bernhard von Stengel, as well as from anonymous referees. All of their comments are gratefully acknowledged. Comments by participants at seminars at Hebrew University (Israel), Technion (Israel), University of Oxford (UK), MEDS, Northwestern (Evanston), DRO, Columbia Business School, Microsoft Research, New England, EC’ 15, Portland, GAMES 2016, Maastricht, IMA, OR Society Conference on Mathematics of Operational Research 2017, Paris Game Theory Seminar, and Ecole Polytechnique were also important, and we thank all of them. This paper builds on the extended abstract published by Pradelski (2015).
- Feller W (1950) An introduction to probability theory and ist applications. Wiley, OxfordGoogle Scholar
- Leshno JD, Pradelski BSR (2018) Efficient price discovery and information in the decentralized assignment game. Working paperGoogle Scholar
- Lewis D (1969) Convention: a philosophical study. Harvard University Press, HarvardGoogle Scholar
- Núñez MNO, Rafels C (2015) A survey on assignment markets. J Dyn Games 2(3–4):227–256Google Scholar
- Pradelski BSR (2015) Decentralized dynamics and fast convergence in the assignment game. In: Proceedings of the 16th ACM conference on economics and computation (EC15) Portland Oregon, p 43Google Scholar
- Tetali P, Winkler P (1991) On a random walk problem arising in self-stabilizing token management. In: Proceedings of the tenth annual ACM symposium on principles of distributed computing, ACM, New York, NY, USA, PODC ’91, pp 273–280Google Scholar
- von Böhm-Bawerk E (1891) The positive theory of capital. Macmillan and Company, LondonGoogle Scholar