Introduction

What is Market-making Middlemen?

• Middlemen/Merchants

  buying/selling price, inventory holdings

• Market-makers/Platforms

  transaction/participation fees, no inventory

Question

How intermediaries determine the intermediation structure?

Short Answer

• Transaction amounts

  (middleman mode is less frictional)

• Competitive pressure

  (market-maker mode decreases competitive pressure)

Model

Model

• Consider a one-period economy
• Agents:
  • $B$ buyers and $S$ sellers
  • One monopolistic intermediary
  • all risk neutral

• Homogeneous goods:
  • unit demands, assumption value 1
  • unit inventory
  • constant marginal production cost, normalized to 0

Decentralized market

• free access
• random search $\lambda^b,\lambda^s \in (0,1)$
• bilateral bargaining, bargaining power $\beta$ for buyers

Centralized market

• Prices are publicly observable: transaction fees $f^b,f^s$, seller price $p^s$, middleman price $p^m$
• Directed search
  • buyers choose which seller to visit
  • no coordinations, limited inventory
  • unmatched buyers/sellers

Timing

1. Two retail markets, a C market and a D market, open. The intermediary announces $\{K,f^b,f^s,p^m\}$.
2. Buyers and sellers simultaneously decide whether to participate in the C market.
3. In C, buyer, sellers and middleman are engaged in a directed search game. In D, agents search randomly.

Search technologies

• Single-market search: traditional retail markets
• supermarkets, brick and mortar shops, etc.
• high search costs, high transportation costs, low durability
• Multi-market search: online shopping, durable goods
• advanced information/search technologies, high durability, long search period

Single-Market search

Two-sideness

• Buyer's expected value to visit a seller

$V^s=\eta^s(1-p^s-f)>\lambda^b\beta$

• Buyer's expected value to visit the middleman

$V^m=\eta^m(1-p^m)>\lambda^b\beta$

Frictions

• buyer’s matching probability at the Middleman

$\eta^m=\frac{\min\{K,x^m\}}{x^m}=1$

in the equilibrium, $K=x^m$

• buyer’s matching probability at a seller

$\eta^s=\frac{1-e^{-x^s}}{x^s}<1$

Definition

• Pure Middleman: $x^m=B$
• Pure Marketmaker: $x^m=0$
• Market-making middleman: $x^m \in (0,B)$

Optimal intermediary

Proposition 1 (Pure middleman)

Given single-market search technologies, the intermediary will not open the platform and will act as a pure middleman with $x^m = K = B$, serving all buyers for sure.

Multi-Market search

Competitive pressure

Timing issue: first mover advantage

Incentive constraint (buyers)

$1-p^m > \lambda^b P^s(x^m) \beta$

$1-p^s -f> \lambda^b P^s(x^m) \beta$

Incentive constraint (sellers)

$p^s > \lambda^s P^b(x^m) (1-\beta)$

Trade off

Intermediary structure influences competitive pressure

$P^s(x^m)$ is increasing in $x^m$

More transactions

Middleman is efficient in matching demand and supply

Less profit per transaction

Middleman creates more competitive pressure

Optimal intermediary

Proposition 2 (Active Market-maker)

Given multi-market search technologies, the intermediary will open a platform and act as:

(1) a market-making middleman if

$\lambda^b \beta \leq 1/2$ or if $\lambda^b \beta > 1/2$ and $B/S \geq c$

(2) a pure marketmaker if

$\lambda^b \beta > 1/2$ and $B/S < c$

Extensions

Extensions

• general matching function in D market
• endowment economy
• competing intermediaries

Endowment economy

Assumption

In the wholesale market, the middleman can access a fraction $\alpha$ of sellers:

$K \leq \alpha S$.

Proposition 3

The intermediation chooses to be a market-making middleman or a pure market-maker with

$x^m \leq K = \alpha S$.

Applications

Amazon

• Amazon faces strong competition from local brick and mortar rivals and especially from eBay.
• Amazon drove physical book and record stores out of business, and many relaunched on Amazon platform.

Trump

• Endownmen economy.
• Brokers in NYC aime at relaxing their resource constraint and increasing their inventory by development.

Conclusion

Conclusion

• A simple framework to study the determination of intermediated market structure.
• Search technology/competitive environment is a critical factor for the emergence of hybrid intermediation.