  We show that the introduction of Tobin taxes in agent-based models of
currency markets can lead to a reduction of speculative trading and reduce the
magnitude of exchange rate fluctuations at intermediate tax rates. In this
regime revenues for the market maker obtained from speculators are maximal. We
here focus on Minority Game models of markets, which are accessible by exact
techniques from statistical mechanics. Results are supported by computer
simulations. Our findings suggest that at finite systems sizes the effect is
most pronounced in a critical region around the phase transition of the
infinite system, but much weaker if the market is operating far from
criticality and does not exhibit anomalous fluctuations.
