The state of New York introduced a bill on Wednesday that would make easier for the state to sue companies if they are seen to be unilaterally violating antitrust issues.

The bill comes on the heels of the House's antitrust hearing when Amazon CEO Jeff Bezos, Alphabet CEO Satya Nadella, Apple CEO Tim Cook, and Facebook CEO Mark Zuckerberg testified.

"Our antitrust laws are about a century old and were built for a different economy," Senator Michael Gianaris, D-NY., the sponsor of the bill, told CNBC's "Squawk Box" on Thursday. "In some ways, what we're trying to do is match what the federal government has the power to do."

Gianaris was outspoken against Amazon's HQ2 move to Long Island City in 2019, his district, a move that earned him the nickname "The Amazon Killer."

He argued existing antitrust laws aren't equipped to tackle the ways tech companies like Google and Amazon interact with their competition today.

"You have behavior that was not contemplated when this law was originally written," Gianaris said. "No one could see a search engine which could prioritize one's own products over competitors, or incentivizing people or punishing them based on the relationship the search engine has."

"We want to give our Attorney General the power, in this new economy, to stifle anti-competitive behavior that is often the result of a single actor acting alone," Gianaris said.

New York can't currently take action against an anti-competitive move unless two companies are collaborating and conspiring to stifle competition. Those actions typically manifest in price-setting or a merger between two companies.

The proposed bill, titled the 21st Century Antitrust Act, would update those laws, so that legal action can be taken against a company if it's shown to be acting in an anti-competitive manner. It would also allow for class-action lawsuits to be brought against companies.

"Federally, you can bring action for unilateral behavior. We're trying to give New York the tools to do the same thing,"Sen. Gianaris said.

The bill would also update the penalties: a violation would be classified as a Class C felony, rather than a Class E felony as it currently stands. The maximum fine would also be changed from $100,000 to $1 million, and the maximum prison sentence from four years to 15 years.

The 21st Century Antitrust Act is unlikely to pass before the end of the year, as the state senate is currently in recess, but it already has the support of New York's Attorney General, Letitia James. "While our state's antitrust laws remain essential to these protections, we support legislation to strengthen them further to meet the challenges of today's economy," James said.

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New York proposes antitrust bill that would make it easier to sue big tech - CNBC