Matching and anonymity

Abstract

Bilateral matching, Frictions, Anonymous trading, Spatial interactions, C78, E00,

Independent random matching

“…Involutions provide a natural formalization for the notion of bilateral matching (e.g., Alós-Ferrer (1999), Aliprantis et al (2006)). In this study, we focus on bilateral matchings where no agent remains unmatched.…”

“…This property may also be seen as natural in a random matching model with a continuum population. Moreover, this property is important as it captures the notion of "anonymity" (see Aliprantis et al (2006)). Properties (P6), (P7), and (P8) have meanings similar to those of (P2), (P3), and (P4) respectively.…”

“…We refer to Aliprantis et al (2006), Alós-Ferrer (1999), Alós-Ferrer (2002), Boylan (1992), Boylan (1995), Duffie and Sun (2007), Gilboa and Matsui (1992), and Molzon and Puzzello (2010). Alós-Ferrer (1999) is the seminal paper about existence of random matching with a continuum population.…”

On the observational equivalence of random matching

“…The state space may depend on the agent, and S g must be de…ned explicitly for a given model. 2 The state space can be a …nite set, a vector space, etc. For instance, s(t; g) could be a vector consisting of various attributes of the agent such as buyer or seller, capital holdings, and so on.…”

“…Additional properties of involutions, bilateral matching, and equivalent counting arguments are discussed in [2,3,23]. We now describe probability distributions on that satisfy conditions M1-M3.…”