Two-Sided Investment and Matching with Multidimensional Cost Types and Attributes

Abstract

Heterogeneous buyers and sellers must make investments before entering a continuum assignment market. I show that efficient ex post contracting equilibria (Cole, Mailath, and Postlewaite 2001b) exist in a general assignment game framework. I then shed light on what enables and what precludes coordination failures. A simple condition—absence of technological multiplicity—guarantees efficient investments for each pair, but a mismatch of agents may still occur. However, using optimal transport theory, I also show that mismatch is heavily constrained in certain multidimensional environments with differentiated agents and no technological multiplicity. Under technological multiplicity, even extreme ex ante heterogeneity need not preclude inefficiencies. (JEL C78, D41, D86)

No Holdup in Dynamic Markets

“…The literature investigating the efficiency of investments under competitive matching (e.g., Cole, Mailath, and Postlewaite 2001b;Peters and Siow 2002;Samuelson 2013 and2017;Nöldeke and Samuelson 2015;Chiappori, Salanié, and Weiss 2017;Chiappori, Dias, and Meghir 2018;Dizdar 2018) focuses on markets featuring a continuum of price-taking agents on each side to turn off the holdup problem and investigate other sources of investment inefficiencies-like coordination failures, participation constraints, and imper-fect information. Our results provide non-cooperative foundations in finite markets for this widely used price-taking assumption, and shows that dynamic entry can be an important force behind price-taking behavior.…”

The Multiplier Effect in Two-Sided Markets with Bilateral Investments

“…Here, γ M > 0 and γ W = 1 − γ M > 0 are constants, and δ M : R + → R + and δ W : R + → R + are non-decreasing, concave, twice continuously differentiable and satisfy δ M (0) = 0 and δ W (0) = 0. 7 The net utility of an unmatched man (woman) with investment β M (β W ) is given by −β M (−β W ).…”

The Multiplier Effect in Two-Sided Markets with Bilateral Investments

“…Following the complete information models of Peters (2007) and Bashkar and Hopkins (2016), the external benefits enter agents' utilities additively, and are modeled via the non-decreasing and type-independent functions δ M and δ W . 8 7 Large parts of our basic equilibrium characterization, including the existence result of Theorem 2 (if the limit conditions are replaced by analogous conditions about limit superiors) apply for arbitrary non-decreasing functions δ M and δ W , but as all our other quantitative results pertain to linear or concave benefits, we focus on this case from the outset. 8 We could easily replace γ M mw and γ W mw by arbitrary smooth and strictly supermodular functions.…”