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Termite Construction and Agent-Based Simulation

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Presentation on theme: "Termite Construction and Agent-Based Simulation"— Presentation transcript:

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 46
47 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 46
47 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 16
17 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 Recombination
1 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.

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