You can, but only at the same price. It's a weird system, especially when markets are located different places, so from each trader or exchange's vantage point, things are in different states. Working around this friction led to an explosion of special order types that some people argue are unfair or overly complex.
In Europe and Asia, there are competitive exchanges, but no rule to force people to route there. There are some guidelines for brokers with customer orders to have a duty of "best execution", but for proprietary traders or professionals, they can do whatever they feel is ideal.
And guess what, there are very few "trade throughs" or cases where markets invert with each other despite lacking such a rule. People usually act in their economic best interest without a law mandating they do so. If it happens, it's an arbitrage that someone will eliminate very quickly.
In Europe and Asia, there are competitive exchanges, but no rule to force people to route there. There are some guidelines for brokers with customer orders to have a duty of "best execution", but for proprietary traders or professionals, they can do whatever they feel is ideal.
And guess what, there are very few "trade throughs" or cases where markets invert with each other despite lacking such a rule. People usually act in their economic best interest without a law mandating they do so. If it happens, it's an arbitrage that someone will eliminate very quickly.