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Paper text:
human activity often takes the form of exchanges .
these exchanges typically consist of goods that can be quantified by value , but also opinions or other types of information may be traded . the former define a market economy .
there have been several proposals to model such markets , see , for example the review by farmer @xcite .
most of the proposed models aim at reproducing the fat tails and volatility clustering in a stock or currency market @xcite .
earlier we have proposed a market model (  fat cat " model ) where agents trade products according to individual price estimates .
these estimates were dynamically adjusted as a function of the trading encounters of each agent @xcite .
the model mentioned above is one of many similar models that could be considered for such a market , each model being distinguished by a strategy that defines which product a buyer should select from a seller and how he should price it later . in the present paper
we study the interplay of a few strategies . the relative performance of these strategies is quantified by the wealth of agents employing them .
we organized the paper by first reviewing the  fat cat " model in section ii .
the extension of this model to the case of other strategies is described in section iii .
then , in section iv we discuss how the model could be extended to cases where agents are able to change their strategies according to their performance and give our concluding remarks .
we picture our model as a cartoon of the trading situations found in a real market . as shown in fig .
1 , this minimalistic model consists of a system where agents trade a set of @xmath0 different products .
each agent @xmath1 is assigned one of three possible strategies selected to be either based on profit ( i.e.   greed " , which is the strategy adopted in the original  fat cat " model ) , on the need for a particular product , or on a random selection without regard to the level of profit or need .    other strategies could be explored ; for example , agents could act as  garbage collectors " , buying whatever product has the lowest possible price . in this paper
we limit ourselves to the three , probably most basic , strategies outlined in fig . 1 .
each of the @xmath2 agents starts with @xmath3 units of goods .
the goods are randomly selected , for each agent , among the @xmath0 different products .
thereby we form the stock @xmath4 of each agent that together with some initial amount of money , @xmath5 define the initial state of the economy .
we describe below the dynamics that arises from the interactions among these agents .    during the time evolution of the system
, each agent @xmath1 has , at each time step , an amount of money @xmath6 , and a stock of the different products @xmath7 , where @xmath8 .
the prices of the different items in the stock of agent @xmath1 are denoted @xmath9 which initially are taken to be integers uniformly drawn in the interval @xmath10 $ ] . in all cases
we have verified that the evolution of the system does not depend on this particular choice .
agents then meet and exchange products and adjust prices .
price adjustment is such that large differences in pricing between agents are lowered , but also such that price differences are induced by some noise when they are small , as in real markets .    as in our simulations for the original  fat cat " model , we assume that at each time step the following procedure takes place :    * * 1 * buyer @xmath11 and seller @xmath12 are selected at random among the @xmath2 agents . if the seller has no products to offer , then another seller is chosen .
* * 2 * the buyer selects a product @xmath13 in the seller s stock according to his strategy @xmath14 .
+ \i ) if strategy @xmath14 is  profit " then he selects the product @xmath13 which maximizes @xmath15 , ( i.e. his profit ) .
+ \ii ) if strategy @xmath14 is  need " then he selects the product @xmath13 which he has the least in his stock ( minimizes @xmath16 ) .
+ \iii ) if strategy @xmath14 is  random " then he selects a random product @xmath13 in the seller s stock for which @xmath17 . + the selected product @xmath13
is called @xmath18 ( best buy ) . * * 3a * if the buyer does not have enough money , ( i.e. if @xmath19 , we return to the first step and choose a new pair of agents . * * 3b * if the buyer has enough money we proceed .
+ if @xmath20 , the transaction is performed at the seller s price .
this means that we adjust : @xmath21 , @xmath22 , @xmath23 , @xmath24 . * * 3c * if @xmath25 , the transaction is not performed . in this case
, the seller lowers his price by one unit , @xmath26 , and the buyer raises his price by one unit , + @xmath27 .
the prices are always non - negative integers . also note that since , as defined in step 3 above , the price offered by the buyer can not be higher than the amount of money it has
, we are not allowing for the agents to get into debt . in case
there are several products that fulfill the selection criterion in 2 , a random one of these is chosen .
one should emphasize that due to the price adjustments performed in unsuccessful encounters , the prices never reach equilibrium , and different agents typically assign different prices to the same product .    to quantify the system ,
we define the total wealth of an agent @xmath1 as the amount of money plus the value of all goods in the agent s possession : @xmath28 the value of product @xmath13 is defined as the average of what all agents consider its value to be : @xmath29 and the value of all of agent @xmath1 s goods , @xmath30 is defined as @xmath31 the  fat cat " model s  profit " rule was studied extensively in our earlier paper .
there it was found to lead to persistency and fat tails in the agents wealth fluctuations with time , hence its name .
we now study the other strategies and their interactions .
the three strategies given above lead to different wealth of the respective agents .
we will now study this in some detail .
our first step is to illustrate how the wealth of the agents gets distributed in a system where all agents employ the same strategy . for that purpose
we consider a system composed of 50 agents , 50 different products .
each agent is given 40 units of products and 20 units of money .
the result , shown in fig .
2 , is that there are appreciable differences in the wealth distribution according to the strategy . for a profit - minded system ( the original  fat cat " model ) , there is a long tail of wealthy agents , which becomes less pronounced when the strategy is based on the stock needs . in this case
there are no rich agents , but instead a large concentration of middle - wealth agents . if the strategy adopted is to buy a random product , the long tail disappears and the middle - wealth peak is shifted to lower values than in the previous case .
the situation can change when the economic conditions , as defined by the number of units of products and money in the economy , are changing .
we will show that there is no best rule for all situations this is shown in fig .
3 , where we have changed the number of units of products , while keeping all other model values the same , in markets composed of equal numbers of agents employing two different strategies . in this case , where @xmath32 , each agent has a few of many possible products , thus representing an antique dealer market where there are many special items and no one can have everything .
we see , in the upper panel , that for this market the  need " strategy , is better than  profit " above 10 units . however , below 10 units , the result is unstable , one strategy leading to better results than the other depending on the initial conditions . in the middle panel
we see that the  random " agents have a higher average wealth than the  profit " motivated ones when the number of units is above 45 , the situation is reversed for a number of units below 35 , and there is unpredictability in between these two values .
finally , the lower panel shows that  need " works better than a  random " strategy for all number of units in the range shown . for other parameter values
, namely when the number of units of products and money is large , the  random " strategy outperforms  need " .
in this last case , namely for @xmath33 , each agent typically has many copies of all products , which represent a mass production market with many copies of few items ; a supermarket world . in this case
, a pairwise comparison of the three strategies shows an interesting situation , depicted in fig . 4 :  need " outperforms  profit " , which outperforms  random " , which outperforms  need " .
so , in this case no strategy is better than both of the other strategies when studied pairwise .    in fig .
5 we explore the triple market further , implementing a market where there is only one agent with  need " strategy among 25 agents with  profit " and 25 agents with  noise " as strategies , so that there are all together 51 agents . without the single  need " strategy ,  random
" would outperform  profit " with a large margin .
a single  need " agent in the system will slowly collect a large fraction of all products in the market .
this is because it has a large competition advantage over the  profit " , which overcompensates its disadvantage to the  random " ones . if the number of  profit " agents were reduced and that of the  random " agents increased , the  need " agent would do worse
this illustrates the fact that the number of agents employing the different strategies is also determinant in the relative success of the agents adopting them .
as we have seen , one may have different strategies for different agents . an interesting direction to extend
this model is to let the agents to select the strategies they adopt in order to improve their performance .
a further extension development would be to allow the strategies themselves to evolve . in the following
we show a preliminary example of how the agents could choose strategies .
a simple mechanism consists in updating , at fixed time intervals , the strategy of the poorest agent in the system .
this agent just changes his present strategy to any of the other two , at random . the resulting time evolution for a system composed of 45 agents initially equally distributed according to their strategies is shown in fig . 6 .
we see that , after an initial transient , the number of agents following the  need " and  random " strategies becomes approximately equal and constant for a considerable period of time , while the  profit " strategy is followed by a small fraction of the agents .
an increase in the  profit " agents leads to a change in the conditions which lead the  random " strategy to almost disappear from the system , to a dominance of  need " , and the persistency of  profit " at a very low level . from the fig .
4 we see that were it not for the existence of  profit "- thinking agents ,  random " would dominate over  need " .
the results shown in fig .
6 also demonstrate that the hierarchy  paper  stone  scissors " illustrated in fig .
4 , for the same system , does not seem to lead , in the time interval considered , to alternations in the number of agents employing each strategy
. there could be several reasons for this .
one is that these changes take longer and longer time to alter enough the market conditions to significantly modify the performance of the different strategies .
another is that while in fig .
4 one measures the average wealth of the agents using each of the three strategies , the criterium for changing strategies is based on the performance of poor agents , _
i.e. _ on the agents wealth distribution in the region close to the origin . as suggested by fig .
2 , a strategy yielding a higher average wealth than another , may also have a larger number of poor agents than the other .
these issues need to be further explored for an appropriate strategy selection procedure and will be discussed in the future .
compared to earlier models of market dynamics the model presented here has some new and related key features : there is local optimization of utility ( estimated market value ) and all trades are done locally without the equilibrizing effects of a global information pool .
this gives arbitrage possibility which drives a dynamic and evolving market .
earlier market models , such as the minority game , have a global information pool , and lack dynamical signals that could be associated with stock market fluctuations .
the evolving boolean network for minority games of paczuski , bassler and corral @xcite , on the other hand , works with local information exchange , but the reward function is still global . also the frame of minority games makes it difficult to treat a multi - product market , which we believe is important for understanding real stock markets .    the model we propose is for a market composed of agents , goods and money ( or people , prices and products ) .
we have demonstrated that such a market easily shows persistent fluctuations of wealth with time , and seen that the persistency is closely related to an interplay of having many products that influence each others trade probability .
a similar result was obtained in the simpler model in @xcite , where it was demonstrated that persistency could arise even without money .
the setup proposed here with agents and products with individual local prices allows for individual strategies of the agents .
this opens for evolution of strategy as a part of the financial market , and we have seen that evolving strategies indeed give a dynamics where wealth is often rapidly redistributed .
we study an economic model where agents trade a variety of products by using one of three competing rules :  need " ,  greed " and  noise " . 
 we find that the optimal strategy for any agent depends on both product composition in the overall market and composition of strategies in the market . 
 in particular , a strategy that does best on pairwise competition may easily do much worse when all are present , leading , in some cases , to a  
 paper , stone , scissors " circular hierarchy .    
 agent - based models ; economic models ; strategic games ;