The Continuous Double Auction Institution

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The Continuous Double Auction Institution

• By P Vytelingum

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Decentralised Systems

• We need to develop tools and methodologies such
  that decentralised systems are
• Robust
• Adaptive
• Autonomous.
• Those distributed systems often require
  allocation policies for scarce resources.
• In our line of work, we look at decentralised
  market-based mechanisms used in those systems for
  resource allocation.

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The Continuous Double Auction

• A symmetric market mechanism that allows buyers
  and sellers to trade
• Market clears continuously whenever a transaction
  is possible
• Traders in the CDA must react in real time to
  maximise their utility

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The Market Optimal Allocation

• Optimal allocation occurs when total profit in
  the market is maximised, which is at the
  equilibrium (price and quantity).

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The Market Competitive Equilibrium

• In the CDA, transaction prices converge to the
  competitive equilibrium, with each agent trying
  to maximise its profit.

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Experimental Economics

• It was shown that, in a CDA, without any central
  control, human traders rapidly and reliably
  converge on the markets theoretical equilibrium.

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Agents vs Humans in the CDA

• A set of experiments with human and software
  traders in a CDA.
• Humans traders were consistently outperformed.
• Consumers are more likely to entrust agents with
  economic decision making if their level or
  performance approach or exceeds the average human
  performance.

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Analysing the CDA using Evolutionary Game-theory
(EGT)

• As software traders swarms in the market, it
  might be interesting to see if it is still
  beneficial for a human trader to rely on a
  software agent.
• EGT provides such an analysis.
• Here, we have an example of the population
  dynamics of a CDA.
• Traders are allowed to choose between 3
  strategies
• For example, what happen when all agents are
  using Kaplan?

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A Variant of the CDA for Constrained Task
Allocation

• Consumers have inelastic demand
• Suppliers have a cost structure consisting of
• A fixed overhead cost
• A constant marginal cost
• Finite production capacities
• We design a decentralised market mechanism for
  the task allocation.

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The Decentralised Mechanism

• A variant of the multi-unit CDA institution.
• All bids and asks are queued in an order book,
  which is cleared continuously.
• Modified to accommodate the inelastic demand a
  consumer has no utility for anything other that
  what it requires.

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The Clearing Process

• Partial clearing of bids is not allowed a bid
  have to be completely allocated or not at all.

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The ZI2 Strategy

• Evaluating the mechanism with a zero-intelligence
  strategy that randomises over price and quantity
  to sell (based on the ZI strategy).
• No limit price as sale quantity cannot be know a
  priori.
• The sellers strategy randomly predicts its sale
  quantity, qj.
• Next, it calculates its limit price, the minimum
  it should sell a unit to avoid a loss (assuming
  it will sell qj. Units)

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The ZI2 Strategy

• The profitable offer price is then randomly
  selected.

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Evaluation of the Mechanism (1)

• Average market efficiency of 83 and a minimum of
  68 when using the ZI2 strategy.

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Evaluation of the Mechanism (2)

• The clearing price was chosen to allow a fair
  distribution of profits between buyers and
  sellers.

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Summary

• We presented a decentralised market mechanism for
  task allocation.
• Buyers with inelastic demand and suppliers with
  constrained cost structure.
• We developed a zero-intelligence strategy to
  evaluate the efficiency of our mechanism.
• In future, we intend to develop strategies with
  more complex behaviours, that learn and adapt
  within the market.

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A Framework for Designing Strategies for
E-Marketplaces.
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The Agent Information Layer (AIL)

• Information the agent requires
• Gathered from the visible (imperfect/incomplete)
  market information
• Private information, e.g. its limit price
• Limited sensory and computational capabilities
  imply agent often can sense only a set of
  information.

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The Knowledge Layer (KL)

• Infers Knowledge from information gathered from
  the market
• It is first requested what knowledge it requires
  and in turn instructs the AIL what information to
  sense in the market.
• Knowledge could be for example the current Sharpe
  ratio of a stock.

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The Behavioural Layer (BL)

• The decision-making component of the strategy
• Instructs the KL what market intelligence it
  requires.
• Behavioural properties categorise as
• no history reactive based only on current market
  conditions
• History
• Non-predictive forms a belief based on past
  experience
• Predictive predicts and adapts to future market
  conditions

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The IKB Framework

• Preliminary work towards a systematic
  multi-layered framework for designing strategies
  for electronic marketplaces.
• For future work, we need to verify our framework
  by applying it to different types of market
  institutions.

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A Risk-Based (RB) Bidding Strategy for the CDA

• A novel bidding strategy for the CDA
• Based on the risk associated with a bid or an ask
  if it were accepted in the market
• The risk-neutral trader will bid at the expected
  transaction price.

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The Bidding Strategy

• The risk model describes how risk attitude
  (towards bidding) affects the bidding behaviour.
• The bidding layer submits a bid or ask.
• The adaptive layer learns the traders risk
  attitude.

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The Risk Model

• The risk model considers the risk factor and the
  estimated equilibrium price.
• A weighted moving average to estimate the
  equilibrium price, p.

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The Risk Function

• Behaviour of model depends on ?
• Sellers cost price and buyers limit price
• Buyers risk function
• Sellers risk function

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The Bidding Layer

• The Bidding Layer submits a bid or an ask.
• Set of rules based on market conditions and a
  target price given by the risk model.

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The Adaptive Layer

• Set of rules used to adapt the traders behaviour
  to the market conditions.
• Triggered by market events.
• A continuous-space learning mechanism increases
  or decreases the traders risk factor based on
  the set of rules.

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Performance in a Heterogeneous Population

• Performance of RB in a population of
  heterogeneous traders, using ZIP and ZI
  strategies.
• Different values of ? gives different
  performances with no apparent correlation.

Table 1. Behaviour of a heterogeneous population
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Defection in a Homogeneous Population

• Incentives for ZI and ZIP agents (in homogeneous
  populations) to defect to an RB strategy.
• No incentive for a trader in a homogeneous RB
  population to deviate to the ZI and to the ZIP
  strategies.

Table 2. Single agent in a homogeneous population
of a different strategy
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Summary

• We described a novel risk-based and adaptive
  bidding strategy.
• We empirically demonstrated the efficiency of our
  strategy in a heterogeneous populations.
• We will explore the consequences of the
  ?-parameter on bidding behaviour.
• We will provide an evolutionary game theoretic
  analysis of the CDA with heterogeneous
  strategies.

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The ARB Strategy

• We develop a highly efficient trading strategy
  for the CDA, that outperforms the current state
  of the art.
• Our strategy adapts its bidding risk and is
  Belief-based. We refer to it as the ARB strategy.
• Consists of 3 components
• A Quote-driven Belief Function
• A Transaction-driven Function
• A Risk-adaptive Utility Function
• ARB uses those 3 components to form an offer.

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The Quote-Driven Belief Function

• We build a belief that an offer will be accepted
  in the market based on the distributions of bids
  and asks (or quotes) submitted in the market.

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The Transaction-Driven Function

• Convergence of transaction prices toward the
  theoretical equilibrium, given by classical
  micro-economic theory.
• The transaction-driven function describe our
  belief of where the theoretical equilibrium lies.
• Modelled as a normal distribution, with the mean
  estimated using the moving average of the history
  of transaction prices.

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The Risk-sensitive Utility Function

• ARB uses a risk-sensitive utility function.
• It adapts its risk to market conditions so that
  it is more risk-averse if it is not making any
  transaction, or more risk-seeking if it can make
  more profit.
• Learning the Risk allows ARB to be more
  competitive in the market.

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The Price Formation

• The offer submitted is the price that maximises
  the product of the expected utility surplus, S
  and the transaction-driven function.
• Purpose of the transaction-driven function is to
  for offer prices closer to the equilibrium price.

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The ARB Performance

• ARB outperforms the most common strategies for
  the CDA in different markets.

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Summary

• We develop a risk-adaptive, belief-based strategy
  that outperform the current state of the art
  strategies in the CDA.
• Our objective is for an ARB agent to secure the
  most profitable transactions, and perform better
  than it would in a centralised mechanism, by
  exploiting other agents.

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Questions?