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

2. 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

3. 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

4. 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

5. 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

6. Structures Formed Domes Pillars Walls Entrances Tunnels
Air conditioning
Fungus farms

7. 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: , 1998.

8. 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

9. 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

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

11. Chambers

12. Recruitment

13. Tunnels

14. Flared Tunnels

15. Narrow Tunnels

16. Dome Entrances Currently no entrance in chambers
New class of “Worker” termites go to and from the queen
Deposit inhibitory trail pheromone

17. Entrances

18. Targets

19. 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

20. 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.

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

22. 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

23. £14 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

24. If you invested it in the S&P 500 index (the stock market), a much riskier bet, how much would you have now?
£1370

25. 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

26. 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.

27. Similar to a continuous double auction
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

28. Example order book Buy Order Sell Order 10 20 30 40 41 42 43 44 45 4647 48 49 50 51 52 53 54 55 56 57 58 59
Price

29. Example order book Buy Order Sell Order 10 20 30 40 41 42 43 44 45 4647 48 49 50 51 52 53 54 55 56 57 58 59
Price
Best Ask
Best Bid
Spread

30. 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?

31. 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

32. 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

33. Orders classified into 12 types based on aggressiveness (Biais et al
Buy Orders
Sell Orders 1
Market larger quantity 7 2
Market equal quantity 8 3
Market smaller quantity 9 4
Limit between quotes 10 5
Limit at quote 11 6
Limit below Quote 12

34. Order Book Mechanism Sell Order Buy Order 10 20 30 11 12 13 14 15 1617 18 19 21 22 23 24 25 26 27 28 29
Price
1,2,3 6 5 4

35. From\To 1 2 3 4 5 6 7 8 9 10 11 12

36. 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 etc.)
Correlation between price movements and order book shape (Huang & Stoll 1994, Parlour 1998 etc.)

37. 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

38. 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…

39. 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

40. Genetic Program Example
Instruction
Program 1
R0 = 2 2
R1 = ps 3
R0 = R0 * R1 4
R1 = R1 – pb 5
Return R0
Results
2ps

41. 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

42. Genetic Programming Mutation
Instruction
Program 1
R0 = 2 2
R1 = ps 3
R0 = R0 * R1 4
R1 = R1 – pb
R0 = R0/5 5
Return R0
Results
2ps
2ps/5

43. Genetic Programming Recombination1
R0 = pb
R0 = 2 2
R1 = ps
R1 = pb 3
R0 = R0 * 5
R0 = R0/R1 4
R1 = R1 – ps
R1 = R1 - 1 5
Return R0
R0 = min(R0,R1) 6
Result
5pb
Min(2/ pb, pb-1)
Min(pb /ps, ps-1) 10

44. 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)

45. Average Bankruptcy Size

46. Wealth Distributions

47. 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.