We analyzed the impact of position-based market maker, which tries to maintain its neutral position, to the competition among stock exchanges by an artificial market simulation approach. In the previous study, we built an artificial market model and investigated for the impact of non-position-based market maker's spread to the markets' shares of trading volumes. However it had the serious problem that the non-position-based market maker is too simple to manage its own position properly and so we could not judge weather the result of previous study is correct or not. Thus in this study, we made a position-based market maker and explored the competition, in terms of taking markets' shares of trading volumes, between two artificial financial markets that have exactly the same specifications except existing a market maker, the non-position-based market maker or the position-based market maker. As a result, we found that the position-based market maker can acquire the share of trading volumes from the competitor even though its spread is bigger than bid-offer-spread of the competitor. Moreover, we revealed that position-based market maker can get a profit even in the situation that its spread or tick sizes of the stock exchanges are small. In addition to that, position-based market maker made a profit in almost all experiments which we conducted in this research by changing its spread and tick sizes of markets. At last, we confirmed that position-based market maker can manage its position properly compared to non-position-based market maker. In conclusion, the position-based market maker can not only supply liquidity to stock exchanges and contribute to acquire the share from the competitor as well as the non-position-based market maker does, but also manage its own position properly and make a profit.