You're starting from the assumption that the manipulator will be effectual.
It is reasonable to expect that arbitrage will tend to make manipulation harder. The basic goal of arbitrage is to recognize open bids that are 'wrong' according to some estimate of the broader market, and to then act on the profitable ones. So in the presence of arbitrage, the manipulative bids that are against the market will quickly disappear.
If a large segment of the market is simply fraudulent, all bets are off. Fraud may well be a better description of what was going on at Mt. Gox than price manipulation (for instance, it isn't really simple price manipulation if their stated customer (dollar) account balances were 10x greater than the paper currency that had ever been deposited).
It is reasonable to expect that arbitrage will tend to make manipulation harder. The basic goal of arbitrage is to recognize open bids that are 'wrong' according to some estimate of the broader market, and to then act on the profitable ones. So in the presence of arbitrage, the manipulative bids that are against the market will quickly disappear.
If a large segment of the market is simply fraudulent, all bets are off. Fraud may well be a better description of what was going on at Mt. Gox than price manipulation (for instance, it isn't really simple price manipulation if their stated customer (dollar) account balances were 10x greater than the paper currency that had ever been deposited).