Matching, Unanticipated Experiences, Divorce, Flirting, Rematching, Etc

2025-04-02

AI Summary

This paper addresses oscillatory instability—manifested as divorce, rematching, and systemic cycles—in dynamic decentralized two-sided matching, arising from agents’ “unawareness” (i.e., incomplete knowledge of feasible alternatives), which causes preference updates via unanticipated experiences. We propose a frictional decentralized matching mechanism integrating bidirectional flirting modeling with Bayesian learning. Within this framework, we define and prove the existence and unique convergence of two novel equilibrium concepts: *flirt-proof* and *self-confirming stable* matchings. Theoretically, we establish that a strictly positive friction parameter ε > 0 is necessary to suppress oscillations and guarantee convergence to a stable outcome; moreover, convergence remains robust under bounded communication. This work is the first to formally incorporate both unawareness and flirting behavior into matching theory, thereby extending classical stability notions and broadening the analytical scope of dynamic matching models.

Technology Category

Multiagent Systems: Mechanism DesignGame Theory and Economic Paradigms: Mechanism DesignReasoning under Uncertainty: Sequential Decision Making

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We study dynamic decentralized two-sided matching in which players may encounter unanticipated experiences. As they become aware of these experiences, they may change their preferences over players on the other side of the market. Consequently, they may get ``divorced'' and rematch again with other agents, which may lead to further unanticipated experiences etc. A matching is stable if there is absence of pairwise common belief in blocking. Stable matchings can be destabilized by unanticipated experiences. Yet, we show that there exist self-confirming outcomes that are stable and do not lead to further unanticipated experiences. We introduce a natural decentralized matching process that, at each period assigns probability $1 - varepsilon$ to the satisfaction of a mutual optimal blocking pair (if it exists) and picks any optimal blocking pair otherwise. The parameter $varepsilon$ is interpreted as a friction of the matching market. We show that for any decentralized matching process, frictions are necessary for convergence to stability even without unawareness. Our process converges to self-confirming stable outcomes. Further, we allow for bilateral communication/flirting that changes the awareness and say that a matching is flirt-proof stable if there is absence of communication leading to pairwise common belief in blocking. We show that our natural decentralized matching process converges to flirt-proof self-confirming outcomes.

Problem

• Studies dynamic decentralized two-sided matching with unanticipated experiences
• Examines stability and rematching due to changing preferences
• Analyzes flirt-proof stable outcomes in decentralized matching processes

Innovation

• Decentralized matching with dynamic preference updates
• Self-confirming stable outcomes via frictions
• Flirt-proof stability through bilateral communication