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By Damien Challet

The Minority online game is a physicist's try and clarify marketplace habit via the interplay among investors. With a minimum set of constituents and drastic assumptions, this version reproduces marketplace ecology between kinds of investors. Its emphasis is on speculative buying and selling and data move. The ebook first describes the philosophy mendacity in the back of the notion of the Minority video game in 1997, and comprises particularly a dialogue concerning the El Farol bar challenge. Then it experiences the most steps in later advancements, together with either the idea and its functions to industry phenomena. This booklet provides a colourful and stylized, but in addition reasonable photograph of ways monetary markets function.

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By Damien Challet

The Minority online game is a physicist's try and clarify marketplace habit via the interplay among investors. With a minimum set of constituents and drastic assumptions, this version reproduces marketplace ecology between kinds of investors. Its emphasis is on speculative buying and selling and data move. The ebook first describes the philosophy mendacity in the back of the notion of the Minority video game in 1997, and comprises particularly a dialogue concerning the El Farol bar challenge. Then it experiences the most steps in later advancements, together with either the idea and its functions to industry phenomena. This booklet provides a colourful and stylized, but in addition reasonable photograph of ways monetary markets function.

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Extra info for Minority Games: Interacting Agents in Financial Markets

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1999; Challet et al. 2000d). Predictability suggests that the behaviour of the Minority Game can be classified in two phases: an information rich or asymmetric phase, and an unpredictable or symmetric phase. This conclusion was put on a firmer basis in Challet and Marsili (1999) and Challet et al. (2000c), which showed that the phase transition takes place exactly where the fluctuations are minimal. It turns out that predictability plays a central role in the Minority Game. Indeed, as we will see in the following chapter, agents behave in such a way as to minimize predictability, in a mathematical form which is closely related to Shannon’s information entropy.

In the asymmetric phase, A|µ = 0 for at least one µ. Hence knowing the history µ(t) at time t, makes the sign of A(t) statistically predictable. A measure of the degree of predictability is given by the function 1 H = P P A|µ 2 = A 2. 21) µ=1 In the symmetric phase A|µ = 0 for all µ and hence H = 0. Challet and Marsili (1999) found that, at fixed M or P , H is a decreasing function of the number N of agents10 (see Fig. 1): this means that newcomers exploit 10 A slightly different quantity θ = 1 P Marsili (1999).

8 The probabilistic nature of agents’ choice does not necessarily imply that the agents randomize their behaviour on purpose. McFadden has indeed shown that Eq. 7) models individuals who maximise an ‘utility’ which has an implicit random idiosyncratic part ηi,s : si (t) = arg max s Ui,s (t) + ηi,s (t) . 8) A computer code for the Minority Game dynamics 33 Summarizing, the dynamics of the simplified Minority Game is described by the following equations: Prob{si (t) = s} = Prob{µ(t) = ν} = e Ui,s (t) s e Ui,s (t) (choices of agents) 1 , ν = 1, .

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