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A Smart-Contract to Resolve Multiple Equilibrium in Intermediated Trade

Daniel Aronoff, Robert M. Townsend

TL;DR

The paper models a two-broker-dealer, two-client repo market and shows that strategic interaction generates multiple equilibria due to inventory externalities. It then constructs a smart-contract framework that coordinates the participants to implement joint profit maximization, leveraging a sequential offer-acceptance protocol and cryptographic tools for privacy and verifiability. The contract relies on an explicit inter-dealer rate relation, $r_{bd}=\frac{1}{2}(r_{rm}+r_{mm})$, and fixed schedules to ensure consistent outcomes, while using fully homomorphic encryption and blockchain verification to preserve privacy and enable public auditability. The work demonstrates how cryptographic market design can improve welfare and efficiency in intermediated markets, with extensions to funding liquidity and client welfare left for future research.

Abstract

We present a model of a market that is intermediated by broker-dealers where there is multiple equilibrium. We then design a smart-contract that receives messages and algorithmically sends trading instructions. The smart-contract resolves the multiple equilibrium by implementing broker-dealer joint profit maximization as a Nash equilibrium. This outcome relies upon several factors: Agent commitments to follow the smart contract protocol; selective privacy of information; a structured timing of trade offers and acceptances and, crucially, trust that the smart-contract will execute the correct algorithm. Commitment is achieved by a legal contract or contingent deposit that incentivizes agents to comply with the protocol. Privacy is maintained by using fully homomorphic encryption. Multiple equilibrium is resolved by imposing a sequential ordering of trade offers and acceptances, and trust in the smart-contract is achieved by appending the smart-contract to a public blockchain, thereby enabling verification of its computations. This model serves as an example of how a smart-contract implemented with cryptography and blockchain can improve market outcomes.

A Smart-Contract to Resolve Multiple Equilibrium in Intermediated Trade

TL;DR

The paper models a two-broker-dealer, two-client repo market and shows that strategic interaction generates multiple equilibria due to inventory externalities. It then constructs a smart-contract framework that coordinates the participants to implement joint profit maximization, leveraging a sequential offer-acceptance protocol and cryptographic tools for privacy and verifiability. The contract relies on an explicit inter-dealer rate relation, , and fixed schedules to ensure consistent outcomes, while using fully homomorphic encryption and blockchain verification to preserve privacy and enable public auditability. The work demonstrates how cryptographic market design can improve welfare and efficiency in intermediated markets, with extensions to funding liquidity and client welfare left for future research.

Abstract

We present a model of a market that is intermediated by broker-dealers where there is multiple equilibrium. We then design a smart-contract that receives messages and algorithmically sends trading instructions. The smart-contract resolves the multiple equilibrium by implementing broker-dealer joint profit maximization as a Nash equilibrium. This outcome relies upon several factors: Agent commitments to follow the smart contract protocol; selective privacy of information; a structured timing of trade offers and acceptances and, crucially, trust that the smart-contract will execute the correct algorithm. Commitment is achieved by a legal contract or contingent deposit that incentivizes agents to comply with the protocol. Privacy is maintained by using fully homomorphic encryption. Multiple equilibrium is resolved by imposing a sequential ordering of trade offers and acceptances, and trust in the smart-contract is achieved by appending the smart-contract to a public blockchain, thereby enabling verification of its computations. This model serves as an example of how a smart-contract implemented with cryptography and blockchain can improve market outcomes.

Paper Structure

This paper contains 42 sections, 17 theorems, 13 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Related literature
  3. A Model of Intermediated Repo Trade
  4. Repo chains
  5. Agent preference functions
  6. The inter-dealer repo rate
  7. BDmm's problem
  8. BDmm carries excess inventories of M into the inter-dealer trade. gapB,Q > 0
  9. BDmm carries no excess inventories of M into the Inter-dealer trade. gapB,Q = 0
  10. Characterizing BDmm's decision problem
  11. BDrm's problem
  12. BDrm carries no excess inventories of T into the inter-dealer trade. gapS,Q = 0
  13. Characterizing BDrm's decision problem
  14. Application to a final-sale market
  15. Multiple Equilibrium
  16. ...and 27 more sections

Key Result

Proposition 2.1

$D_{r_{mm}} = S_{r_{rm}}$ in equilibrium, i.e. neither $BD$ will carry excess inventories into the inter-dealer trade.

Figures (12)

  • Figure 1: First and Second-Leg Repo Chain
  • Figure 2: $BD_{mm}$ Problem
  • Figure 3: $BD_{rm}$ Problem
  • Figure 4: Balanced Inter-dealer Trade Surface
  • Figure 5: Sequence of $r_{mm}$ steps
  • ...and 7 more figures

Theorems & Definitions (39)

  • Proposition 2.1: No excess inventory in Inter-dealer trade Equilibrium
  • Definition 3.1: Unique Balance
  • Definition 3.2: Inter-dealer trade Equilibrium under perfect knowledge
  • Definition 3.3
  • Proposition 3.1
  • proof
  • Proposition 3.2: Notional complimentarity
  • proof
  • Definition 3.4
  • Theorem 3.1: Existence of Inter-Dealer Pure Strategy Equilibrium Client repo rate Pairs
  • ...and 29 more