From market games to real-world markets

We present a dynamical theory of a multi-agent market game, the so-called Minority Game (MG), based on crowds and anticrowds. The time-averaged version of the dynamical equations provides a quantitatively accurate, yet intuitively simple, explanation for the variation of the standard deviation ('volatility') in MG-like games. We demonstrate this for the basic MG, and the MG with stochastic strategies. The time-dependent equations themselves reproduce the essential dynamics of the MG.Agent-based games have great potential application in the study of fluctuations in financial markets. Challet and Zhang's Minority Game (MG) [1,2] offers possibly the simplest example and has been the subject of much research [2]. The MG comprises an odd number of agents N choosing repeatedly between option 0 (e.g. buy) and option 1 (e.g. sell). The winners are those in the minority group, e.g. sellers win if there is an excess of buyers. The outcome at each timestep represents the winning decision, 0 or 1. A common bit-string of the m most recent outcomes is made available to the agents at each timestep [3]. The agents randomly pick s strategies at the beginning of the game, with repetitions allowedeach strategy is a bit-string of length 2 m which predicts the next outcome for each of the 2 m possible histories. Agents reward successful strategies with a (virtual) point. At each turn of the basic MG, the agent uses her most successful strategy, i.e. the one with the most virtual points. Here we develop a dynamical theory for MG-like games based on the formation of crowds and anticrowds.The number of agents holding a particular combination of strategies can be written as a D × D × . . . (s terms) dimensional matrix Ω, where D is the total number of available strategies. For s = 2, this is simply a D × D matrix where the entry (i, j) represents the number of agents who picked strategy i and then j. The strategy labels are given by the decimal representation of the strategy plus unity, for example the strategy 0101 for m = 2 has strategy label 5+1=6. Ω is fixed at the beginning of the game ('quenched disorder') and can represent either the full strategy space or the reduced strategy space [1], depending on the choice of D. Σ is another time-independent matrix, containing all the strategies in the required space in their binary form: Σ r,h+1 describes the prediction of strategy r given the history h (where h is the decimal corresponding to the m-bit binary history string).We introduce a vector n(t): this contains the number of agents using each strategy at time t, in order of increasing strategy label. The vector S(t) contains the virtual score for each strategy at time t in order of increasing strategy label. The vector R(t) lists the strategy label in order of best-to-worst virtual points score at time t; if any strategies are tied in points then the strategy with the lower-value label is listed first. The vector ρ(t) shows the rank of the strategy listed in order of increasing strategy label at time t. Hence R(t) and ρ(t) can...

show abstract

“…[7]). Our efforts to develop such simplified market games in order to describe real-world financial markets are described elsewhere [8].…”

mentioning

confidence: 99%

Crowd-anticrowd theory of multi-agent market games

et al. 2001

Self Cite

View full text Add to dashboard Cite

show abstract

“…In contrast to the basic Minority Game (MG) [11], this variable-N model has the realistic feature of accounting for agents' confidence [13,14]. Furthermore the variable-N model can be used to generate statistical and dynamical features similar to those observed in financial markets (archetypal examples of complex systems) [13,2]. Therefore, demonstration of predictability of extreme events in the present multi-agent model would open up the exciting possibility of predictability of extreme events in real-world systems.…”

mentioning

confidence: 99%

“…a financial market [13], whose dynamics are well-described by the multi-agent game for a fixed unknown parameter set m, N, τ, T and an unknown specific realization of initial strategy choices. We call this our 'black-box' game.…”

mentioning

confidence: 99%

Predictability of Large Future Changes in a Competitive Evolving Population

2001

View full text Add to dashboard Cite

The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes ('extreme events'). We study the large, internal changes produced in a generic multi-agent population competing for a limited resource, and find that the level of predictability actually increases prior to a large change. These large changes hence arise as a predictable consequence of information encoded in the system's global state.01.75.+m, 02.50. Le, 05.40.+j, 87.23.Ge Typeset using REVT E X 1

show abstract

“…reported on a technique based on multi-agent games which has potential use in predicting future movements of financial time-series. In their articles, a "third-party" game is trained on a "black-box" time-series, and then run into the future to extract next step and multi-step predictions [1,2,3]. They used minority game as the third party game.…”

Section: Introductionmentioning

confidence: 99%

Predictability of Shanghai Stock Market by Agent-based Mix-game Model

Gou

2005

SSRN Journal

View full text Add to dashboard Cite

Abstract-This paper1 reports the effort of using agent-based mix-game model to predict financial time series. It introduces simple generic algorithm into the prediction methodology, and gives an example of its application to forecasting Shanghai Index. The results show that this prediction methodology is effective and agent-based mix-game model is a potential good model to predict time series of financial markets.

show abstract

From market games to real-world markets

Cited by 122 publications

References 21 publications

Crowd-anticrowd theory of multi-agent market games

Crowd-anticrowd theory of multi-agent market games

Predictability of Large Future Changes in a Competitive Evolving Population

Predictability of Shanghai Stock Market by Agent-based Mix-game Model

Contact Info

Product

Resources

About