Diffusion and localization of relative strategy scores in the Minority Game

We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase ($\alpha\equiv P/N\gtrsim 1$) of the basic Minority Game using sign-payoff, with $N$ agents holding two strategies over $P$ histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent's strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score $x\in\mathbb{Z}$ of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at $x=0$ for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates $x/\sqrt{N}$ and $t/N$ the distributions are uniquely given by $\alpha$ and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase

How to improve robustness in Kohonen maps and display additional information in Factorial Analysis: application to text mining

This article is an extended version of a paper presented in the WSOM'2012 conference [1]. We display a combination of factorial projections, SOM algorithm and graph techniques applied to a text mining problem. The corpus contains 8 medieval manuscripts which were used to teach arithmetic techniques to merchants. Among the techniques for Data Analysis, those used for Lexicometry (such as Factorial Analysis) highlight the discrepancies between manuscripts. The reason for this is that they focus on the deviation from the independence between words and manuscripts. Still, we also want to discover and characterize the common vocabulary among the whole corpus. Using the properties of stochastic Kohonen maps, which define neighborhood between inputs in a non-deterministic way, we highlight the words which seem to play a special role in the vocabulary. We call them fickle and use them to improve both Kohonen map robustness and significance of FCA visualization. Finally we use graph algorithmic to exploit this fickleness for classification of words

Colour reverse learning and animal personalities: the advantage of behavioural diversity assessed with agent-based simulations

Foraging bees use colour cues to help identify rewarding from unrewarding flowers, but as conditions change, bees may require behavioural flexibility to reverse their learnt preferences. Perceptually similar colours are learnt slowly by honeybees and thus potentially pose a difficult task to reverse-learn. Free-flying honeybees (N = 32) were trained to learn a fine colour discrimination task that could be resolved at ca. 70% accuracy following extended differential conditioning, and were then tested for their ability to reverse-learn this visual problem multiple times. Subsequent analyses identified three different strategies: ‘Deliberative-decisive’ bees that could, after several flower visits, decisively make a large change to learnt preferences; ‘Fickle- circumspect’ bees that changed their preferences by a small amount every time they encountered evidence in their environment; and ‘Stay’ bees that did not change from their initially learnt preference. The next aim was to determine if there was any advantage to a colony in maintaining bees with a variety of decision-making strategies. To understand the potential benefits of the observed behavioural diversity agent-based computer simulations were conducted by systematically varying parameters for flower reward switch oscillation frequency, flower handling time, and fraction of defective ‘target’ stimuli. These simulations revealed that when there is a relatively high frequency of reward reversals, fickle-circumspect bees are more efficient at nectar collection. However, as the reward reversal frequency decreases the performance of deliberative-decisive bees becomes most efficient. These findings show there to be an evolutionary benefit for honeybee colonies with individuals exhibiting these different strategies for managing resource change. The strategies have similarities to some complex decision-making processes observed in humans, and algorithms implemented in artificial intelligence systems

Effects of Diversity on Multi-agent Systems: Minority Games

We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. The games can be used to model economic markets, ecosystems or distributed control. Diversity of initial preferences of strategies is introduced by randomly assigning biases to the strategies of different agents. We find that diversity among the agents reduces their maladaptive behavior. We find interesting scaling relations with diversity for the variance and other parameters such as the convergence time, the fraction of fickle agents, and the variance of wealth, illustrating their dynamical origin. When diversity increases, the scaling dynamics is modified by kinetic sampling and waiting effects. Analyses yield excellent agreement with simulations.Comment: 41 pages, 16 figures; minor improvements in content, added references; to be published in Physical Review

Models of Financial Markets with Extensive Participation Incentives

We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealths. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive-sumness of the players' wealths provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealth of both the players and market-makers. New players survive in the market if the evolutionary rate is sufficiently slow. We test the applicability of the model on real Hang Seng Index data over 20 years. Comparisons with other models show that our model has a superior average performance when applied to real financial data.Comment: 17 pages, 16 figure

Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information

We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents. In the limit $N\to\infty$ we calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\alpha>\alpha_c$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\alpha<\alpha_c$ the stationary state is shown to be non-unique. For $\alpha\to 0$ we analyse our equations in leading order in $\alpha$, and find asymptotic solutions with diverging volatility \sigma=\order(\alpha^{-{1/2}}) (as regularly observed in simulations), but also asymptotic solutions with vanishing volatility \sigma=\order(\alpha^{{1/2}}). The former, however, are shown to emerge only if the agents' initial strategy valuations are below a specific critical value.Comment: 15 pages, 6 figures, uses Revtex. Replaced an old version of volatility graph that. Rephrased and updated some reference