Stochastic strategies in the Minority Game
  We show analytically how the fluctuations (i.e. standard deviation) in the Minority Game (MG) can decrease below the random coin-toss limit if the agents use more general, stochastic strategies. This suppression of the standard deviation results from a cancellation between the actions of a crowd, in which agents act collectively and make the same decision, and an anticrowd in which agents act collectively by making the opposite decision to the crowd. 
M. Hart, P. Jefferies and N.F. Johnson (Oxford University) and P.M.   Hui (Chinese University of Hong Kong)