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the minority game ( mg ) , introduced by challet and zhang  @xcite as a generalisation of arthur s ` el farol ' problem  @xcite , has gained much popularity as a simple yet realistic model of the workings of financial markets .
a great variety of work has since been done on the mg  @xcite , leading eventually to an analytic solution  @xcite ; these insights have proven particularly useful in justifying the mg as a realistic model of real market situations  @xcite .    the interactive minority game ( img ) proposes to further this use of the mg in modelling real markets by using the mg to try to gain insight into the behaviour of humans in a simplified market situation .
individual humans compete against the traditional computer - controlled agents , whose characteristics can be fine - tuned through our understanding of the traditional mg : the human player can be presented with a very inefficient and easy - to - predict market , or with one that is much more complex and difficult .    in creating an interface for the game , our emphasis was on simplicity and ease of use
: the game should be playable by anyone , from a seasoned mg researcher to someone who comes across the website at random .
a number of aspects of the interface may therefore seem a little strange to those who have experience of the mg , and so in this paper we explain the mechanical workings - behind - the - scenes that go into the img : firstly , the interface , and secondly , the setup and parameters behind the different choices of game .
fundamentally , the interactive minority game is a minority game like any other .
a group of @xmath0 agents must choose between two actions , @xmath1 ( ` buy ' ) or @xmath2 ( ` sell ' ) , with the intention to make the opposite choice to the majority of agents ; agents decisions are based on the knowledge of which was the minority or majority action of the last @xmath3 turns .
however , in order to make the game a little easier to play , we have had to change the presentation ( though not the underlying game ! ) a little for the sake of the human player .
the human player not only has the advantage of a greater memory ( denoted by @xmath4 ) than the computer players , but is also given a choice between two different methods of presentation for the information about the game history ; in addition , rather than asking the human player for an action ( ` buy ' or ` sell ' ) , we ask them for a prediction on the direction the market is going to take , which corresponds to an action in the underlying game . in this section we explain ( and , we hope , justify ) in detail all these aspects of the interface .
imagine being confronted by the string of 1 s and 0 s that is given to the regular agents !
it is not a particularly pleasant thought , and the human player will clearly demand more .
we have provided two different solutions to the problem . before we continue , let us recall a few aspects of the mg . at each time
step @xmath5 , each agent @xmath6 takes an an action @xmath7 , which allows us to define the @xmath8 action @xmath9 :    @xmath10    this allows us to define the first , simpler view of the game history : the _ binary viewpoint _ , a set of spins corresponding to @xmath11 in the the last @xmath4 turns of the game .
this is of course identical in information content to the aforementioned string of 1 s and 0 s , but looks nicer !
the more interesting viewpoint follows from an idea suggested by johnson _ et .
@xcite of a price level , @xmath12 , in the mg , defined by    @xmath13    where @xmath14 is the market liquidity .
we have used this in our _ chart viewpoint _ , literally a price - chart recording the past values of @xmath12 ( see fig .  [ fig:2 ] ) .    the price - chart view of the game .
the price changes proportionally to the global action @xmath9 of agents ( eq .  [ eq:2 ] ) ; the player must predict whether the market will rise or fall .
note that the last action is highlighted for the player . ]    clearly , the binary viewpoint is more suited to games where the player s gain is also binary , i.e.  where @xmath15 , and the price - chart view is more suited to games with a linear payoff , @xmath16 .
this is the practise we have followed in our ready - made games .
however , the option to create a custom game allows the user to ignore our advice if s / he feels like it !
the reader may have noticed that , rather than being asked to make a choice ( ` buy ' or ` sell ' , @xmath1 or @xmath2 ,  ) , the human player is asked to ` _ _ predict which way you think the market is going to go _ _ ' .
that is , the user is asked to _ predict the majority action _ , and their own action ( the opposite ) is inferred from this  we ask the human player for a prediction @xmath17 and an amount bet on this prediction , @xmath18 ( their _ weight _ or _ market impact _ ) , and their action is then taken to be @xmath19 .
we apologise if this is perhaps a little confusing for those familiar with the mg ! our concern , as we noted in the introduction , was to make the game simpler for those who have never encountered the mg before . ` what way do you think the market will go ? ' seemed to us a simpler question than , say , ` would you like to buy or sell ( do the opposite of what you think everyone else will do ) ? ' in addition , those unused to the mg might reasonably ask , like andersen and sornette in a recent paper  @xcite , questions such as , ` why does buying hurt me if the market keeps rising ? ' we would rather avoid such problems !    in summary : although it is a little hidden from view , the player still has to try and perform the minority action .
;-)      the game interface consists of a series of php files that interact with an underlying c program ; the latter calculates the actions of all the computer - controlled agents , and calculates all the relevant and interesting quantities ( such as predictability ) .
we hope that the reader will forgive us if we are coy about revealing any more ( in particular , about revealing source code ) ; we are willing to reveal the workings - behind - the - scenes but there are a few rabbits - up - our - sleeve that we would like to keep from players for now , so as to make the game more interesting !
the interactive minority game offers a number of possibilities for the human player to pick from . as well as a variety of ` standard ' , ready - made games
, there is the option to create a custom game by choosing from various parameters . for those well - versed in mg lore
, this could no doubt do with some extra explanation .
parameters particular to the human player are denoted by a subscript asterisk ( @xmath20 ) .      to begin with ,
let us summarise the basic parameters of the mg : we have a homogeneous population of @xmath0 agents with memory @xmath3 , each with @xmath21 strategies .
this gives us @xmath22 as the size of the space of histories given to agents , and we can then define the control parameter @xmath23 . it is this parameter @xmath24 which determines the type of market : a low value creates an extremely inefficient market , easily predictable by the smart human , while a high value of @xmath24 creates a market whose behaviour is close to randomness .
the most efficient market ( and therefore most difficult to play ) , i.e.  the market with the minimal value of standard deviation @xmath25 , lies somewhere in the middle at the critical point @xmath26  @xcite . for the purposes of our games ( custom or standard ) ,
we have chosen to make @xmath3 and @xmath24 variables , with other parameters being calculated from these two .
as we have already noted , the human player enjoys the benefit of a larger memory , @xmath27 , than the computer - controlled agents ; we have chosen to set @xmath28 for the binary view and @xmath29 for the price - chart view .
we have also added a parameter particular to the img for the human player : the player s _ weight _ or _
market impact_. recall from 
[ sec : predict ] that at each time @xmath5 the player is asked for a prediction @xmath30 on the direction the market will take , and the amount they bet on this , @xmath31 .
their action is then taken to be , @xmath32    put simply , this amounts to the human player taking an action @xmath33 rather than @xmath34 ; i.e. , the player chooses to have a market impact equivalent to that of @xmath35 normal agents .
the player s gain per turn is then also proportional to @xmath35 .
depending on the market phase , this can be an advantage or a disadvantage : it brings the potential of a greater reward if the player can correctly predict the market , but with the potential of a far greater loss if s / he can not .
we have also used the concept of _ minimum weight _ , @xmath36 , where we require that @xmath37 .
we can force the human player to act on a larger scale than the typical agent 
equivalent , perhaps , to the actions of a large investment bank rather than an individual trader .
the other new parameter introduced , for custom games , is the length of the _ introductory period _ , @xmath38 .
this is the length of time that the computer - controlled agents play by themselves before the human player joins the game .
a long value allows the agents to adapt to the statistically stationary state of the game , while if @xmath38 is low , the players start off `` stupid '' , not knowing which of their strategies is better . in the more difficult games ( efficient markets ) , a such a low value is essential as a high value of @xmath38 makes it completely impossible for a human to compete !
the img allows the player both to pick from a variety of ` standard ' , ready - made games and to create their own custom game .
the total choices available to the player are as follows : their _ minimum weight _
, @xmath36 ; the _ market phase _ , determined by @xmath24 ; the _ agent memory _ , @xmath3 ; the display mode ( see  [ sec:2 - 1 ] ) ; the payoff ( binary or linear ) ; and , in the custom game , the length of the introductory period , @xmath38 .
the * custom game * allows the choice of a full range of parameters , including some that are not used in our standard games .
minimum weight can be small ( @xmath39 ) , medium ( @xmath40 ) or large ( @xmath41 ) absolute values ; the market phase varies from extremely crowded ( @xmath42 ) to crowded ( @xmath43 or @xmath44 ) , the critical point ( @xmath45 ) and anticrowded ( @xmath46 or @xmath47 ) .
@xmath3 can be 1 , 2 , 3 , 4 , 6 or 8 ; the introductory period can be the full period ( @xmath48 ) , or it can be short ( 200 ) or very short ( 5 ) .
the * standard games * were set up to create a variety of different market experiences for the human player .
_ beginners _ is exactly that : a nice and easy game , with @xmath49 , @xmath42 and @xmath39 .
this is designed simply as a friendly introduction to the img and should not be taken too seriously !    the _ newbie traders _ game is a little trickier , with with @xmath39 and @xmath50 as before , but now with @xmath51 .
_ day traders _ is again trickier , with @xmath52 , @xmath42 and @xmath39 , while _ chartists _ ups the ante still further with @xmath51 .
_ wall street gurus _ throws the player into a difficult market at the critical point , with @xmath53 , @xmath54 and @xmath39 .
_ mission impossible _ is literally that  the player must struggle with a large @xmath40 and an anticrowded market ( @xmath55 ) full of very intelligent agents ( @xmath56 ) .
all standard games use the price - chart view with a linear payoff .
while clearly the fundamental aim of the img ( apart from being a fun distraction for the econophysics community ! )  is to investigate the behaviour of humans in market situations , we should perhaps specify a bit more precisely what we are looking for . here
are a few of the questions we have in mind :    * what sort of performance do we see from humans in different types of market ( crowded , anticrowded , critical  ) ? * how do humans make their decisions ?
do they stick to one strategy or vary their behaviour often ? * how much information do human players give to the market ? *
do they take into account their market impact ?    in conclusion
, we hope that the img , while a very simple and easy game , might provide a fascinating window into what is actually going on inside the heads of real , human , economic agents  surely one of the ultimate econophysical goals !
999999999 d.  challet and y .- c .
zhang , _ physica _ * 246a * , 407 ( 1997 ) .
the _ interactive _ minority game ( img ) is an online version of the traditional minority game in which human players can enter into competition with the traditional computer - controlled agents . through the rich ( and , 
 importantly , analytically understood ) behaviour of the mg , we can explore humans behaviour in different kinds of market  crowded , efficient , critical  with a high degree of control . to make the game easily understandable even to those who are encountering it for the first time , we have presented the game with a rather simplified interface ; in this working paper we explain the underlying technical aspects for those who have experience with the traditional mg .