Presentation on theme: "Leeds University Business School Termite Construction and Agent-Based Simulation Dan Ladley, Leeds University Business School and School of Computing"— Presentation transcript:
Leeds University Business School Termite Construction and Agent-Based Simulation Dan Ladley, Leeds University Business School and School of Computing firstname.lastname@example.org www.comp.leeds.ac.uk/danl
Leeds University Business School 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
Leeds University Business School 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
Leeds University Business School 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: BlueprintLeader PlanTemplate
Leeds University Business School 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
Leeds University Business School Structures Formed Domes Pillars Walls Entrances Tunnels Air conditioning Fungus farms
Leeds University Business School 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.
Leeds University Business School 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
Leeds University Business School 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
Leeds University Business School Agent Building Behaviour Probability of building when queen pheromone level lies in a particular range Crude physics Newly placed material gives off cement pheromone
Leeds University Business School 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
Leeds University Business School 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.
Leeds University Business School Agent Based Models Allow the investigation of: Heterogeneous individuals Bounded rationality Complex relationships The time path or dynamics of a system
Leeds University Business School 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
Leeds University Business School 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? £14
Leeds University Business School If you invested it in the S&P 500 index (the stock market), a much riskier bet, how much would you have now? £1370
Leeds University Business School 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
Leeds University Business School 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.
Leeds University Business School 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
Leeds University Business School Example order book Buy Order Sell Order 10 2010203010 4041424344454647484950515253545556575859 Price
Leeds University Business School Example order book Buy Order Sell Order 10 2010203010 4041424344454647484950515253545556575859 Price Best Ask Best Bid Spread
Leeds University Business School 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?
Leeds University Business School 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
Leeds University Business School 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
Leeds University Business School Orders classified into 12 types based on aggressiveness (Biais et al. 1995) Buy OrdersSell Orders 1Market larger quantity7 2Market equal quantity8 3Market smaller quantity9 4Limit between quotes10Limit between quotes 5Limit at quote11Limit at quote 6Limit below Quote12Limit below Quote
Leeds University Business School Order Book Mechanism Sell Order Buy Order 10 2010203010 11121314151617181920212223242526272829 Price 1,2,3 456
Leeds University Business School From\To123456789101112 1 2 3 4 5 6 7 8 9 10 11 12
Leeds University Business School 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.)
Leeds University Business School 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
Leeds University Business School 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…
Leeds University Business School 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
Leeds University Business School Genetic Program Example InstructionProgram 1R 0 = 2 2R 1 = p s 3R 0 = R 0 * R 1 4R 1 = R 1 – p b 5Return R 0 Results2p s
Leeds University Business School 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
Leeds University Business School Genetic Programming Mutation InstructionProgramInstructionProgram 1R 0 = 21 2R 1 = p s 2 3R 0 = R 0 * R 1 3 4R 1 = R 1 – p b 4R 0 = R 0 /5 5Return R 0 5 Results2p s Results2p s /5
Leeds University Business School Genetic Programming Recombination Program 1Program 2Program 1Program 2 1R 0 = p b R 0 = 21R 0 = p b R 0 = 2 2R 1 = p s R 1 = p b 2R 1 = p s R 1 = p b 3R 0 = R 0 * 5R 0 = R 0 /R 1 3 R 0 = R 0 * 5 4R 1 = R 1 – p s R 1 = R 1 - 14 R 1 = R 1 – p s 5Return R 0 R 0 = min(R 0,R 1 )5 Return R 0 6 6 Result5p b Min(2 / p b, p b -1)ResultMin(p b /p s, p s -1)10
Leeds University Business School 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)
Leeds University Business School Average Bankruptcy Size
Leeds University Business School Wealth Distributions
Leeds University Business School 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.