A New Stochastic Strategy for the Minority Game

We present a variant of the Minority Game in which players who where successful in the previous timestep stay with their decision, while the losers change their decision with a probability $p$. Analytical results for different regimes of $p$ and the number of players $N$ are given and connections to existing models are discussed. It is shown that for $p\propto 1\mathrm{/}N$ the average loss ${\sigma }^2$ is of the order of 1 and does not increase with $N$ as for other known strategies.