Download Minority Games: Interacting Agents in Financial Markets by Damien Challet PDF

By Damien Challet

The Minority video game is a physicist's try and clarify industry habit via the interplay among investors. With a minimum set of elements and drastic assumptions, this version reproduces industry ecology between types of investors. Its emphasis is on speculative buying and selling and data circulation. The e-book first describes the philosophy mendacity in the back of the notion of the Minority online game in 1997, and contains particularly a dialogue in regards to the El Farol bar challenge. Then it reports the most steps in later advancements, together with either the speculation and its functions to industry phenomena. This booklet offers a colourful and stylized, but additionally sensible photograph of ways monetary markets function.

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Extra resources for Minority Games: Interacting Agents in Financial Markets

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E. p = 1/2 as, for example, in Fig. 3), depending on the value of µ. This means that the value of µ(t) contains some information on A(t) because it makes possible a better than random prediction of the minority side. 34 for S = 2). The transition separates a symmetric (α < αc ) from an asymmetric phase (α > αc ). The symmetry which is broken is that of the average A|µ of A(t) conditional on the history µ. 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.

These results leave us with a number of open questions that a theory of the Minority Game should address. 1 39 Information and predictability The quantity H captures predictability in the Minority Game. To make this statement more precise, it is helpful to make explicit the connection with standard tools of information theory, such as the Shannon entropy. Back in Savit’s paper (Savit et al. 1999), information was quantified in a ‘bar graph’ with the probabilities p µ = Prob{A(t) > 0|µ(t) = µ} plotted against µ.

Suppose that agents base their decisions on the last M attendance sizes. With N agents, the attendance can take N + 1 values each time. This makes (N + 1)M possible combinations of information about the past. If strategies are based on a prediction of the attendance given the past history, as in Arthur’s paper, we have N +1 possible predictions for each combination of information M and hence (N + 1)(N +1) possible prediction for any combination. Hence there are M (N + 1)(N+1) possible predictor strategies.

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