Two-Sided Matching Models

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Definition of the Subject

This article describes the basic elements of the cooperative and non‐cooperative approaches fortwo-sided matching models and analyzes the fundamental differences and similarities between someof these models.

Basic Definitions

Feasible outcome: 

is an outcome that is specified by the rules of the game. In thediscrete case, a feasible outcome is a feasible matching μ or at least corresponds toa feasible matching. The usual definition is the following. The matching μ is feasibleif it matches every agent to an allowable set of partners and\( { \mu(f) \in Ch_{f} (\mu(f) \cap W) } \)and\( { \mu(w) \in Ch_{w}(\mu (w) \cap F) } \)for every\( { (f,w) \in F \times W } \). Then, if preferences areresponsive, every matched pair is mutually acceptable. An implication of this definition is thata feasible outcome is always individually rational.

In the continuous case, the rules of the game may specify, for example, whether the agentsnegotiate their payoffs individually within each ...