In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game with number of strategies for each agent S=2 and "fake" market histories . The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of  the Minority Game  , by means of the game parameter \sigma^{2 is performed. An " (\alpha,\sigma^{2) -matrix" containing, given options' moneyness and maturities, values of the parameters \alpha and \sigma^{2} that make the theoretical option price agree with the market price is constructed. } We conclude that  the asymmetric phase of the Minority Game with \alpha close to \alpha_c is coherent with options implied volatility market.
In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game . The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Canonical Minority Game , by means of their characteristic parameters, is performed. ) -matrix" containing, given options' moneyness and maturities, values of the parameters \alpha and \sigma^{2} that make the theoretical option price agree with the market price is constructed. } We conclude that for both games the asymmetric phase with characteristic parameters close to critical ones is coherent with options implied volatility market.
R
with number of strategies for each agent S=2 and "fake" market histories
and a Grand Canonical Minority Game
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both
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and the Grand Canonical Minority Game
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the game parameter \sigma^{2
their characteristic parameters,
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An " (\alpha,\sigma^{2
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for both games
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of the Minority Game with \alpha close to \alpha_c
with characteristic parameters close to critical ones