Thepilotstudyoftheheterogeneousmultiagentcomplexsystems.doc

the pilot study of the heterogeneous multiagent complex systemsliu liying，xu bingzhenfaculty of science, ningbo university, ningbo（315211）e-mail：.abstractin this paper we study the heterogeneous multiagent complex systems base on the minority game andevolutionary minority game in stock markets. in this model, not only the number of the agents change, but also the amount invested of every agent at every time step change too. under the underlying idea, we find they are disciplinary that distributions of the survival probability with risk coefficient or action preference, and distribution of the total assets with risk coefficient by the simulationkeywords: minority game; heterogeneous multiagent complex systems; risk coefficient; asset distribution; survival probabilitypacc：0175, 0520d, 7120h1.introductionagent-based models of complex adaptive systems16,17 are attracting significant interest across many disciplines1.they can be applied to different fields such as: stock markets,alternative roads between two locations and in general problems in which the players inthe minority win. one of the most studied models in the field of complex adaptive systems is the minority game(mg) proposed by d. chellet and y. c. zhang2,3,4 andits evolutionary version(emg)5,6,7,8,9,10,11,12.the minoritygame comes from the so-called el farol bar problem by w. b. arthur. the underlying idea is competition for limited resources, so the agents compete to be in the minority by making decisions based on global information created by the agents themselves. while, in the evolutionary formulation of the model(emg), the agents are allowed to evolve their strategies according to the past experiences. in the other words, each agent tries to learn from his past mistakes and adjust his strategy in order to survive or perform better. in this letter, we proposed a heterogeneous multiagent complex systems model, which based on the minority game and its evolutionary version.the mg15 is a simple model of interacting agents, and the emg is evolving based on themg. so we can introduce the emg simply.the basic model of the emg consists of n (odd) agents, each having some finite number of strategies. at each time step, each agent has to choose independently one of the two kinds of actions, such as buying and selling the asset in a financial market. early studies of the emg were restricted to situations in which the prize-to-fine ratio r was assumed to be equal to unity. all agents have taken their actions independently, those who are in the minority group win and acquire a point. a remarkable conclusion deduced from the emg 5 is that a population of competing agents tends to self-segregate into opposing groups characterized by extreme behavior. however, in many real life situations the prize-to-fine tatio r may take a variety of different values11. a different kind of strategy may be more favored in such situations. in fact, our daily experience indicates that in difficult situations humans tend to be confused and indecisive.2.model2.1 model introduction- 5 -based on this qualitative expectation, we have recently extended the exploration of the mg and various extensions of the model5,13,14 including emg. then, it is proposed that the heterogeneous multiagent complex systems model is applying in the stock markets. it has several aspects different from mg and emg. first, the number of populations is not invariable. this means the agents of the heterogeneous multiagent complex systems are eliminated through contest in the trading system. secondly, investment of every agent is change. in prevenient models, every agent invest invariable assets. but, in the heterogeneous multiagent complex systems model, each agent invest assets with different proportions.2.2 model describingthe heterogeneous multiagent complex systems consist of n (integer) agents, each agent must choose buy or sell stocks at each time step in the stock markets. in this paper we hypothesis each agent has two parts assets. in order to model the heterogeneous multiagent complex systemsi = 1, 2,k, nlet consider a set of agentswhere n z(integer). agent i at time t hastwo part assets: one part is cash assets am(i, t ) , the other part is stock assets as(i, t) . each agent has initial values of the assets aream(i, 0) = d ran1as(i, 0) = d ran2where d is a constant by presumed,ran1andran2(1) (2)are random numbers.if a certain agent has bought stocks, his cash assets reduce and stock assets increase, by contraries, if the agent has sold stocks, then his cash assets increase and stock assets reduce. it is worthy of attention that each agent invest different proportional assets in transaction. so we introduce a random number -called risk coefficient ri , where is the investment of each agent in proportion to his total assets. when n agents have all done their choices, their assets will change. at the same time, the stock price will be affect by all assets of buying and selling in every transaction.at each time t the stock price are determined bypt = bs / ss(3)where bs is total assets of all agents buy stocks, ss is total assets of all agents sell stocks.and wheret = 0 ,p0 = 1.if a certain agent buy stocks, the agents assets becomeasi, t +1 = asi, t + r ami, t / ptami, t +1 = ami, t r ami, t if a certain agent sell stocks, the agents assets becomeasi, t +1 = asi, t r asi, t ami, t +1 = ami, t + r asi, t pt(4)(6) (7)(5)the market is evolving, and the agents have the ability of abiding learning. so each agent continuously adjust his strategy by induction and consequence in order to adapt the change of the market, which is restricted to their mastered information and knowledge. if an agent performs too bad and lose his all assets, he will be eliminated through contest in the market. this means thenumber of the agents will decrease in the market. if an agent has cash assets but hasnt stock assets, he can not sell stocks but can buy more stocks. on the contrary, if an agent has stock assets but hasnt cash assets, he can not buy more stocks but can sell stocks.2.3 simulate resultswe focus on three quantities,rd(ri)andsd(ri),with the risk coefficient ri ,and gd( g )with the action preference g . hererd(ri)is the survival probability of theagents with the risk coefficient ri ;sd(ri)is the asset distribution with the risk coefficient ri ;gd( g )is the survival probability of the agents with the action preference g .1.0000.999rd(ri)0.9980.9970.9960.0 0.2 0.4 0.6 0.8 1.0rifig.1 the survival probability of the agents as a function of the risk coefficient ri .the results are for n=10000 agent, d =100.each point represents an average value over 5000 runs and 5000/10000/100000 time steps per run.where nst means time stepfigure 1 shows the distribution of the survival probability of the agents for different ri values after many transactions in uniform financial markets. the curve demonstrates the survival probability of the agents falls with the risk coefficient increase. so the risk lovers are eliminated easily through contest, then the risk averters survive easily.250nst=5000nst=10000nst=50000200150sd(ri)1005000.0 0.2 0.4 0.6 0.8 1.0rifig.2 the asset distribution as a function of the risk coefficient ri . the results are for n=10000 agent,d =100.each point represents an average value over 5000 runs and 5000/10000/100000 time steps per runin fig. 2, we display the total assets (including cash assets and stock assets) distribution of the survival agents for different ri values. we find that the total assets distribution exits a peak( occurring at risk values less than 0.5). the results demonstrate the total assets of the agents concentrate upon the risk averters, then the risk lovers are eliminated through contest. we can know that the curves become higher in virtue of larger ri value, and the peak values move to left. these imply that the agents will be eliminated easier through contest if the risk lovers the degree of risk preference is higher, and the total assets will be concentrated upon more cautious(the valueof ri is smaller) agents.1.000.95gd(g)0.900.850.800.750.0 0.2 0.4 0.6 0.8 1.0gfig.3 the survival probability of the agents as a function of the action preference g .the results are forn=10000 agent, d =100.each point represents an average value over 5000 runs and 100000 time steps per runfigure 3 displays the distribution of the survival probability of the agents for different gvalues. the curve is symmetric aboutg = 0.5 , with peaks aroundg = 0 andg = 1. theresult is insensitive to the initial distribution of g values. surprisingly, agents who either always follow or never follow what happened last time, generally perform better than cautious agents using an intermediate value of g .(6)references1for a detailed account of previous work on agent_based models such as the minority game, see http:/www.unifr.ch/econophysics.2d. challet, y. c. zhang, emergence of cooperation and organization in an evolutionary game j . physica a.1997, 246 (3) : 407-418.3d. challet, y. c. zhang, on the minority game: analytic and numerical studies j . physica a. 1998, 256 (4) :514-532.4y. c. zhang, toward a theory of marginally efficient market j . physica a, 1999, 269 (1) : 30-44.5n. f. johnson, p. m. hui, r. johnson, and t. s. lo. self-organized segregation within an evolving population. phys rev lett, 1999, 82(16): 33603363.6t. s. lo, p. m. hui, and n. f. johnson. theory of the evolutionary minority game. phys rev e, 2000, 62(3):43934396.7n. f. johnson, p. m. hui, and t. s. lo, philos. trans. r. soc. londo