Leeds University Business School Termite Construction and Agent-Based Simulation Dan Ladley, Leeds...

Leeds University Business School

Termite Construction and Agent-Based Simulation

Dan Ladley,

Leeds University Business School and School of Computing

[email protected]

www.comp.leeds.ac.uk/danl


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


Computing Applications

Insects have evolved solutions to challenging distributed coordination problems which have been successfully adapted to real world systems.

Locating food sources -> Shortest path algorithms

Building nests -> Nano-technology, Space Exploration

Dividing labour -> Task Allocation problems

Brood Sorting -> Graph partitioning, data analysis


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


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


Structures Formed

Domes

Pillars

Walls

Entrances

Tunnels

Air conditioning

Fungus farms


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, 353:1561-1576, 1998.


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


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


Agent Building Behaviour

Probability of building when queen pheromone level lies in a particular range

Crude physics

Newly placed material gives off cement pheromone


Chambers


Recruitment

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 20 40 80 160 320 640 1280

Workers

Dep

osit

s p

er

wo

rker


Tunnels


Flared Tunnels


Narrow Tunnels


Dome Entrances

Currently no entrance in chambers

New class of “Worker” termites go to and from the queen

Deposit inhibitory trail pheromone


Entrances


Targets


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


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.


Agent Based Models

Allow the investigation of:

Heterogeneous individuals

Bounded rationality

Complex relationships

The time path or dynamics of a system


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


A Game:

It’s 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?

£14


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

£1370


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


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.


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


Example order book

Buy 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


Example order book

Buy 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

Best Ask

Best Bid

Spread


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?


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


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


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


Order Book Mechanism

Sell Order

Buy Order

10

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

1,2,3456


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


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.)


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


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…


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


Genetic Program ExampleInstruction Program

1 R0 = 2

2 R1 = ps

3 R0 = R0 * R1

4 R1 = R1 – pb

5 Return R0

Results 2ps


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


Genetic Programming MutationInstruction 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


Genetic Programming RecombinationProgram 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


Analysis of Margin Constraints

Vary β from 0 to 1 in increments of 0.1

β = 0 corresponds to no buying on margin

β =1 corresponds to having no restriction on capacity to buy (unrealistic)


Average Bankruptcy Size


Wealth Distributions


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.

Leeds University Business School Termite Construction and Agent-Based Simulation Dan Ladley, Leeds...

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