Market Design with Blockchain Technology

Katya Malinova and Andreas Park

We first presented this paper in June 2016 ...

... and for 1 year people told us that trading of blockchain "stocks" was years away

 

How did these guys put it ...?

 

Initial Coin Offerings are now a reality

  • Available tokens for trading (Coinmarketcap, August 19, 2017)
    • 182
  • Capital raised from mid-2016 to date:
    • $1.3B (NYT July 27, 2017)
  • Market cap (Coinmarketcap, August 19, 2017)
    • ~$8.3B

What is different?

1. Multiple trading protocols are possible

User-facing exchange mask

Fully Decentralized, "OTC",

Peer-to-Peer Exchange

What is different?

2. High Level of Transparency

See transactions between "addresses" (="IDs")

What is different?

3. You can tell who owns what

To sum up: What is different?

  1. Exchange-trading and Peer to Peer is possible
    • current world peer-to-peer -- through intermediaries
      • a dealer/market maker is on one side of trade
      • parties know who they are trading with
    • technology enables frictionless value transfer
  2. Past transactions are visible
    • may be able to see frequent "traders"
    • caveat: traders = wallets/addresses = IDs (return to this)
  3. Current holdings are visible
    • may be able to tell who the "whales" are

Informational environment changes drastically

What do you know and what do you not know in OTC?

What do you know and what do you not know in Peer-to-Peer?

Research Question

How does the design of ledger transparency and identifier-usage with possible P2P interactions affect trading behavior and economic outcomes?

  • different ledger transparency regimes are possible
    • ledger is visible to all
    • ledger is hidden (from some)
  • different identifier-usage regimes are possible
    • mandate single IDs per entity
    • allow multiple IDs
      • traders may obfuscate their holdings by using numerous accounts/IDs (Buterin 2015)

Who benefits and loses under which regime?

Model Ingredients

  • Risky asset, value normally distributed 
  • Two large investors

    • Each period one is hit with size Q=1 liquidity shock.

    • Other can absorb the shock at zero cost.

  • ​Continuum of 1/   small investors
    • ​trade with probability       at "public" price
    • each period, mass 1 wants to buy, mass 1 wants to sell
  • Infinitely many trading periods
N(0,\sigma^2)
N(0,σ2)N(0,\sigma^2)
\rho\le1/2
ρ≤1/2\rho\le1/2
\rho
ρ\rho

Disclaimer:

  • no asymmetric information 
  • => our results need not be applicable to all asset classes
\rho
ρ\rho

Model Ingredients:
Trading and Timing

 

  • When hit with a shock, the "liquidity trader" (LT) may:
    • trade peer-to-peer (OTC)  (with small and/or large  peers)
      • refer to the other large as "liquidity provider" (LP)
    • trade with a risk-averse intermediary at​

       
      • Intermediary's inventory I "shifts" the public price
    • net-trades with intermediary = inefficient transfer of risk 
  • All unfilled positions clear with the intermediary at the end of a stage game.
p(q)=\frac{\kappa \sigma^2}{N}\ (-I+q) \equiv \frac{\ell}{2} (q-I)
p(q)=κσ2N (−I+q)≡ℓ2(q−I)p(q)=\frac{\kappa \sigma^2}{N}\ (-I+q) \equiv \frac{\ell}{2} (q-I)

Model Ingredients: Direct Costs

  • Data processing/complexity to contact mass q
  • Quadratic cost to contact mass q of IDs:
    • cost c is a loss to aggregate welfare
    • pay        and trade quantity
  • Linear mining/validation cost:
    • pay       to trade with     IDs
\rho q
ρq\rho q
\frac{c}{2} q^2
c2q2\frac{c}{2} q^2
\gamma q
γq\gamma q
q
q q

Disclaimer:

  • no asymmetric information 
  • => our results need not be applicable to all asset classes

Model Ingredients:
Indirect Costs: Front-Running

  • Modelling Mechanics of Front-Running:
    1. LT to LP: Buy quantity Q at price p?
    2. LP buys Q from intermediary and moves the "public price" P to
    3. LP to LT: "sell you Q at price ≫ p?"
  • Front-runner pays validation costs.
P+ \ell/2 \times Q
P+ℓ/2×QP+ \ell/2 \times Q

Model Ingredients: Transparency of Ownership

  1. Full transparency = common knowledge of who is large
    • assume single ID (since validation costs increase in # of IDs)
  2. No transparency
    • only single ID allowed
  3. No transparency (ownership cannot be inferred)
    • continuum of IDs (to obfuscate ownership)

Benchmark:
fully transparent (single ID) ownership

Requires a system design choice:

  • allow an entity (individual, investment fund) only a single ID per instrument
  • possible with private blockchain

Fully Transparent Ownership

  • Key feature: large traders are identifiable.

  • Large trader LT may:

    • Trade  with small investors.

    • Trade with the intermediary.

    • Approach the other large trader LP.

 

Option 1:
Trade with small investors and intermediary

  • Contact mass x of investors such that 

complexity cost

current market price paid to small

costly trading with intermediary

validation cost

\max_x -\frac{c}{2}x^2-\rho \gamma x-x\rho\frac{\ell}{2}\times (-I) - (1-\rho x)(1-\rho x -I)\times\frac{\ell}{2}.
maxx−c2x2−ργx−xρℓ2×(−I)−(1−ρx)(1−ρx−I)×ℓ2.\max_x -\frac{c}{2}x^2-\rho \gamma x-x\rho\frac{\ell}{2}\times (-I) - (1-\rho x)(1-\rho x -I)\times\frac{\ell}{2}.

Option 2:
Approach other Large Trader

  • (+) ability to locate/contact the LP

    • escape complexity and validation costs

    • avoid price impact of trade with risk-averse intermediaries

  • (-) reveal info about the trading needs
    • [model choice]: LT may get “front-run” by LP.

​

Pros & Cons

Front-Running

  • Single shot: LP always extracts all surplus (or would front-run). 
  • Repeated setting: 
    • Front-running is punished in subsequent periods via “trigger strategy” punishment.
    • Deviation → large traders avoid each other; trade with small and intermediary forever.

The Benchmark Equilibrium

  1. In a repeated game, "social norms" have bite and front-running can always be avoided.
  2. LT always trades with LP.
  3. LT and LP share the cost savings.
  4. Price concession
    • For small discount factor (≈ infrequent interaction) price concession is necessary.
    • For large enough discount factors (≈ frequent interactions), price concession = 0 is an equilibrium.

Opaque Single ID ownership

Equilibrium

  • The optimization problem is similar to that in Option 1 under full transparency. 
  • The optimal mass of IDs to contact is independent of the intermediaries inventories/public price.
  • Mass x* depends on:
    •   : probability of small traders accepting the offer
    •   : the (il-)liquidity of the intermediated market
    •   : complexity/data processing costs.
\rho
ρ\rho
x^*=\max\{0, \frac{\ell \rho}{\ell \rho^2+c} - \frac{\rho\gamma}{\ell \rho^2+c}\}
x∗=max{0,ℓρℓρ2+c−ργℓρ2+c}x^*=\max\{0, \frac{\ell \rho}{\ell \rho^2+c} - \frac{\rho\gamma}{\ell \rho^2+c}\}
\ell
ℓ\ell
c
cc
  • When the  validation cost is not too large,              , the liquidity trader trades with both continuum & intermediaries
\gamma < \ell
γ<ℓ\gamma < \ell

Opaque multi-ID ownership

Closest and native to "public" blockchains:

  • anyone can participate anonymously
  • can create as many accounts as I want
  • describe by Ethereum founder as simple solution to achieve privacy
  • private blockchains can choose to organize themselves like this

Acceptance Probabilities: depend on LP's decision

small traders

large trader

small traders

large trader

small traders

large trader

filled

unfilled


Opaque Single ID

Opaque Multi-ID: LP accepts

Opaque Multi-ID: LP rejects

\rho
ρ\rho
\frac{2\rho}{1+\rho}>\rho
2ρ1+ρ>ρ\frac{2\rho}{1+\rho}>\rho
\frac{\rho}{1+\rho}<\rho
ρ1+ρ<ρ\frac{\rho}{1+\rho}<\rho

Decision problem LT

accept offer

submit large amount to continuum

  • (small) price concession to entice larger trader (but also paid to and "wasted on" small traders)
  • larger search costs
  • no price concession
  • expensive interaction with intermediary
  • smaller complexity cost

Decision problem LP

submit large amount to continuum

front run

  • incurs validation fee when front-running

Characterizing the Equilibrium

  • Search for equilibrium where LP accepts offers & doesn't front-run.
  • To avoid front-running price concession p>0 may be necessary
    • need to offer p to all peers, large and small.
  • Trigger strategy: offer p=0 & large rejects 
    • => "over-trading" with the intermediary
  • Validation costs:
    • do not affect the LT directly: with dispersed ownership, has to pay both for trades with peers and with intermediary.
    • matter for front-runner => has to pay unrecoverable sunk cost to move price

Equilibrium & More

Result 1: There exists an equilibrium with no front-running where

  • LP accepts
  • price concession = 0

provided

  • the discount factor is large enough
    • = frequent interactions.
  • or the intermediated market is sufficiently liquid
    • = front running not very profitable (small quantity and low price advantage)
  • or validation costs are sufficiently high
    • = sunk cost for front-running too high.

Equilibrium & More

Result 2 (numerical): For small discount (=infrequent interaction) factors, the equilibrium with no front-running where LP accept does not exist. Then:

  • In equilibrium, LT offers p = 0 to the continuum, and
  • LP's IDs reject the offer.
     

=> over-trading with intermediary

  • Observation: an increase in the validation cost may curb front-running.

 

 

Comparing the designs

Observations

 

  • Trading with the intermediary is socially inefficient 
    • to avoid this cost, large traders must interact
    • if not, there is always an imbalance of traders who trade with the intermediary
  • Trades between small and large traders cause complexity costs
  • By construction, payoffs under the full transparency benchmark are highest.
  • The trade-off for opaque regimes are:
    • complexity cost vs
    • intermediation cost

Comparing multi- vs single-ID opaque designs

 

  • Finding 1:
    • When large traders do not trade with each other, the welfare is the same in both opaque systems, irrespective of the ID-ownership setup.
  • Finding 2:
    • When large do trade with one another with multi-ID ownership, the welfare in this setting  is higher than in the single-ID setting.

Payoffs to Large Traders

Finding 3:

The following relations hold for the average equilibrium stage payoffs of large traders.

  1. When large traders do not trade with each other with multi-ID ownership, their equilibrium payoffs in this setting are lower than those the opaque single-ID setting.
     
  2. When large traders trade with each other with multi-ID ownership at p =0, their equilibrium payoffs in this setting dominate those in the opaque single-ID setting.
     

Finding 4: (Numerical)

There exist parametric configurations such that large traders trade with each other at p > 0 in the multi-ID ownership setting, but their average equilibrium payoff in the opaque single-ID setting is higher.

 

Summary

  1. "Back office" settlement has important front office implications!
    • with peer-to-peer there are critical design choices
      • Who can see the ledger?
      • How are virtual identities managed?
  2. Findings:
    • Transparent ledger with single IDs is welfare optimal and has lowest wealth redistribution (almost by construction)
    • Between (A) public blockchain solution with multiple IDs and (B) private, non-transparent ledger with single IDs:
      • public blockchain privacy solution has higher aggregate welfare
      • but does not necessarily lead to higher payoffs for large investors.

Market Design with Blockchain Technology - SHoF August 2017

By Andreas Park

Market Design with Blockchain Technology - SHoF August 2017

This is a set of slides that my co-author Katya Malinova used for a presentation of my paper with Katya Malinova on our paper "Market Design with Blockchain Technology". This iteration was presented on August 22, 2017. The deck has been designed for a 25 minute presentation.

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