  We consider a prediction problem with two experts and a forecaster. We assume
that one of the experts is honest and makes correct prediction with probability
$\mu$ at each round. The other one is malicious, who knows true outcomes at
each round and makes predictions in order to maximize the loss of the
forecaster. Assuming the forecaster adopts the classical multiplicative weights
algorithm, we find upper and lower bounds for the value function of the
malicious expert. Our results imply that the multiplicative weights algorithm
cannot resist the corruption of malicious experts. We also show that an
adaptive multiplicative weights algorithm is asymptotically optimal for the
forecaster, and hence more resistant to the corruption of malicious experts.
