Termite Construction and Agent-Based Simulation

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Termite Construction and Agent-Based Simulation

• Dan Ladley,
• Leeds University Business School and School of
  Computing

danl_at_comp.leeds.ac.uk www.comp.leeds.ac.uk/danl
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• Social Insects
• Social insects such as termites, ants and bees
  successfully accomplish many complex tasks
  through cooperation.
• These include
• Locating food sources
• Building nests
• Dividing labour
• Brood Sorting

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• Computing Applications
• Insects have evolved solutions to challenging
  distributed coordination problems which have been
  successfully adapted to real world systems.
• Locating food sources -gt Shortest path
  algorithms
• Building nests -gt Nano-technology, Space
  Exploration
• Dividing labour -gt Task Allocation problems
• Brood Sorting -gt Graph partitioning, data
  analysis

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• Termite nest formation
• Many individual termites participate in the
  construction of termite nests. Due to the large
  size of the next relative to individual termites
  and the number of individuals involved this is a
  difficult coordination problem.
• The most common ways of coordination are
• Blueprint Leader
• Plan Template

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• Stigmergy
• The above methods do not work for termites
  instead they employ stigmergy. Cues in the
  environment encourage termites to make certain
  behaviours which in turn effect the environment
  effecting future behaviours.
• Termites respond to many environmental cues.
  These include
• Pheromones
• Cement, Queen, Trail
• Temperature
• Air Movements
• Humidity

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• Structures Formed
• Domes
• Pillars
• Walls
• Entrances
• Tunnels
• Air conditioning
• Fungus farms

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• Previous Model
• Demonstrated the existence of pillars, chambers,
  galleries and covered paths
• No consideration of logistic factors or inactive
  material

• E. Bonabeau, G. Theraulaz, J-L. Deneubourg, N.
  Franks, O. Rafelsberger, J-L. Joly, S. Blanco. A
  model for the emergence of pillars, walls and
  royal chambers in termite mounds. Philosophical
  Transactions of the Royal Society of London,
  Series B, 3531561-1576, 1998.

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• Agent Based Model
• Three dimensional discrete world
• Populated by a finite number of termites
• Three pheromone types
• Cement given off by recently placed material
• Trail given off by moving termites
• Queen given off by stationary queen
• Diffusion through finite volume method

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• Agent Movement
• May move to any adjacent location as long as
• There is no building material present
• The new location is adjacent to material
• Movement influenced by cement pheromone
• Roulette wheel selection based on pheromone
  gradients
• Random Movement with probability 1/Gradient

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• Agent Building Behaviour
• Probability of building when queen pheromone
  level lies in a particular range
• Crude physics
• Newly placed material gives off cement pheromone

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Chambers
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Recruitment
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Tunnels
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Flared Tunnels
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Narrow Tunnels
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• Dome Entrances
• Currently no entrance in chambers
• New class of Worker termites go to and from the
  queen
• Deposit inhibitory trail pheromone

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Entrances
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Targets
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• Pros and Cons of this model
• Reproduces results seen in nature
• Importance of logistic constraints
• Applications in real situations space
  exploration, nano-tech
• Simplistic movement strategy
• Artefacts due to tessellation of world
• No accounting for castes of termites

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• Agent-based modelling is employed in other
  fields, in particular it is key to current
  research in epidemiology, transport studies and
  defence.
• Many fields investigate problems involving many
  interacting individuals engaging in potentially
  complex and changing relationships which are
  frequently difficult to analyse with more
  traditional techniques.

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• Agent Based Models
• Allow the investigation of
• Heterogeneous individuals
• Bounded rationality
• Complex relationships
• The time path or dynamics of a system

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• Agent-Based Models
• These models have draw backs
• They do not provide proofs only demonstrations of
  sufficiency
• There are typically many ways to model any given
  situation
• Parameters, parameters and more parameters

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• A Game
• Its January 1926 you have 1 to invest
• If you invested it in US Treasury bills, one of
  the safest bets around, and reinvested all of the
  proceeds how much would you have now?

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• If you invested it in the SP 500 index (the
  stock market), a much riskier bet, how much would
  you have now?

1370
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• Now suppose that each month you were able to
  divine which would do better and invested
  everything in that, how much would you have?

2,296,183,456
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• Motivation
• In order to predict what is going on in financial
  market it is vital to separate the effect of the
  market mechanism and individual behaviour.
• The order book market mechanism is employed (with
  variations) in the majority of the worlds major
  financial institutions.

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• Order book markets
• Similar to a continuous double auction
• Traders submit orders to the market
• Market Orders execute immediately at the best
  available price for the specified quantity
• Limit Orders are added to the order book at the
  specified quantity and price
• Trade results in limit orders being removed from
  the book

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• Example order book

Buy Order Buy Order Sell Order Sell Order

10
10 20 10 20 30 10 10
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Price Price Price Price
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• Example order book

Buy Order Buy Order Sell Order Sell Order

10
10 20 10 20 30 10 10
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Price Price Price Price
Best Ask
Best Bid
Spread
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• Understanding order book markets
• Analytical work - Difficult to maintain
  analytical tractability
• Empirical and experimental work - Difficult to
  separate trader strategy from the effect of the
  market mechanism
• Simulation work how should the traders agents
  behave?

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• Solution - Zero Intelligence
• Traders modelled to behave randomly, consequently
  any effects observed in the data are due to the
  market mechanism. Those not observed are then
  dependant on individual behaviour.

Observed Behaviour Effect of Trader Strategy Effect of Market Mechanism
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• Agent-Based Model
• 100 traders each initially allocated 50 units to
  either buy or sell with reservation prices
  stepped between 0 and 100
• Each time step one trader selected at random to
  submit an order for a random number of units at a
  random price drawn from a uniform integer
  distribution constrained by the limit prices of
  the traders units
• With a set probability new traders enter and
  leave the market each time step

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• Orders classified into 12 types based on
  aggressiveness (Biais et al. 1995)

Buy Orders Sell Orders
1 Market larger quantity 7 Market larger quantity
2 Market equal quantity 8 Market equal quantity
3 Market smaller quantity 9 Market smaller quantity
4 Limit between quotes 10 Limit between quotes
5 Limit at quote 11 Limit at quote
6 Limit below Quote 12 Limit below Quote
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• Order Book Mechanism

Sell Order Sell Order Buy Order Buy Order
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10 20 10 20 30 10 10
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Price Price Price Price
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From\To 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
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• Also predicts
• Details of the bid ask spread
• Intra-book spreads
• Quantities available at the quotes
• Effect of changes of the tick size
• Importance of the tips of the order book
  (Griffith et al. 2000 etc.)
• Correlation between price movements and order
  book shape (Huang Stoll 1994, Parlour 1998
  etc.)

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• Conclusions
• Much of the order dynamics typically observed in
  markets can be explained as a consequence of the
  order book market mechanism
• In many cases trader strategy may not be the
  dominant force in observed market behaviour
• However this is only half of the story we still
  need to understand the strategies employed by
  traders

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• Model as before, except
• The agents are now trading a financial asset
  (e.g. a stock in a company) and money
• They are paid dividends and interest and must
  consume a fraction of their wealth each time step
• They are subject to margin constraints a limit on
  the amount of money a trader may borrow to some
  fraction of there net-worth
• And the traders have strategy

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• Genetic Programs
• Programs are provided with the 8 input parameters
  (information about the market)
• Two outputs, the quantity and price are returned
• Quantity Rounded to Integer Values
• Price Rounded to 0,1 then mapped to
  10000,20000
• Three registers for variable manipulation are
  provided

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• Genetic Program Example

Instruction Program
1 R0 2
2 R1 ps
3 R0 R0 R1
4 R1 R1 pb
5 Return R0
Results 2ps
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• Genetic Programming Tournaments
• One Tournament per trading period
• 4 Individuals selected at random
• Fitness equal to net worth
• 2 Least fit individuals have their strategies
  replaced

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• Genetic Programming Mutation

Instruction Program Instruction Program
1 R0 2 1 R0 2
2 R1 ps 2 R1 ps
3 R0 R0 R1 3 R0 R0 R1
4 R1 R1 pb 4 R0 R0/5
5 Return R0 5 Return R0
Results 2ps Results 2ps/5
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• Genetic Programming Recombination

Program 1 Program 2 Program 1 Program 2
1 R0 pb R0 2 1 R0 pb R0 2
2 R1 ps R1 pb 2 R1 ps R1 pb
3 R0 R0 5 R0 R0/R1 3 R0 R0/R1 R0 R0 5
4 R1 R1 ps R1 R1 - 1 4 R1 R1 - 1 R1 R1 ps
5 Return R0 R0 min(R0,R1) 5 R0 min(R0,R1) Return R0
6 Return R0 6 Return R0
Result 5pb Min(2/ pb, pb-1) Result Min(pb /ps, ps-1) 10
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• Analysis of Margin Constraints
• Vary ß from 0 to 1 in increments of 0.1
• ß 0 corresponds to no buying on margin
• ß 1 corresponds to having no restriction on
  capacity to buy (unrealistic)

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• Average Bankruptcy Size

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• Wealth Distributions

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• Conclusions
• There exists an optimal level of market
  regulation reducing bankruptcy
• Traders strategies depend heavily on the level of
  borrowing allowed
• Agent-based models can provide insights into
  these systems unachievable with other techniques.