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: Blueprint Leader Plan Template 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 Chambers Leeds University Business School Recruitment 1.8 1.6 Deposits per worker 1.4 1.2 1 0.8 0.6 0.4 0.2 0 10 20 40 80 160 320 640 1280 Workers Leeds University Business School Tunnels Leeds University Business School Flared Tunnels Leeds University Business School Narrow Tunnels Leeds University Business School Dome Entrances Currently no entrance in chambers New class of “Worker” termites go to and from the queen Deposit inhibitory trail pheromone Leeds University Business School Entrances Leeds University Business School Targets 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: 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 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 Sell Order 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 Leeds University Business School Example order book Buy Sell Best Ask Order Order Best Bid 10 10 20 10 Spread 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 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 Observed = Effect of + Effect of Behaviour Trader Market Strategy Mechanism 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. 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 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 Leeds University Business School Order Book Mechanism Sell Buy Order Order 6 5 4 1,2,3 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 Leeds University Business School 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 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 Instruction Program 1 R0 = 2 2 R 1 = ps 3 R0 = R0 * R1 4 R 1 = R 1 – pb 5 Return R0 Results 2ps 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 Instruction Program Instruction Program 1 R0 = 2 1 R0 = 2 2 R1 = ps 2 R 1 = ps 3 R0 = R 0 * R1 3 R 0 = R0 * R1 4 R 1 = R 1 – pb 4 R0 = R0/5 5 Return R0 5 Return R0 Results 2ps Results 2ps/5 Leeds University Business School Genetic Programming Recombination Program 1 Program 2 Program 1 Program 2 1 R 0 = pb R0 = 2 1 R 0 = pb R0 = 2 2 R 1 = ps R1 = pb 2 R 1 = ps R 1 = pb 3 R0 = R0 * 5 R0 = R0/R1 3 R0 = R0/R1 R0 = R0 * 5 4 R 1 = R 1 – ps R 1 = R 1 - 1 4 R1 = R1 - 1 R 1 = R 1 – 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 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.