They definitely want to increase your productivity, you are right. Your productivity drives their revenue forward. They are willing to contribute small amount of that revenue for giving you free food. But do you really want to be like that? Work harder for free food?

I don't think the purpose of free food is to incentivize employees to work harder. It's to let employees have lunch in the office without having to leave. As mentioned several times in the comments here, employees at companies that provide this option tend to like it.

it is to make employees have lunch in the office without letting them leave.

None of these tech companies make anyone eat the lunch and they certainly let employees leave. Do some research before posting.

Indeed they don't lock employees inside the building. Indeed it's far from slavery. It's wrong word. Rather it's exploiting of employees by using cheap tricks.

> giving employees perks in the hope that it will increase their productivity

By "their", you mean the company? Because employees receive the same salary no matter their productivity.

Slavers also fed their slaves, property requires upkeep costs.

> Because employees receive the same salary no matter their productivity.

No, in fact they typically do not. Drop your productivity to zero and see how your salary holds up.