not only is the 'free market' a myth (as FourWinds has pointed out) but the notion that such competition is limited to the epoch known as capitalism is also equally flawed.
There is a reason why it is known as CAPITALism, rather than COMPETITIONism. It's what Marx called the 'law of value', which (very very basically) relates to the way labour power is turned into a commodoity to be traded at the lowest value, and that one of the key ways to lower it's value is by 'constantly revolutionising the means of production' (but not the mode of production) and introducing new technologies so that less and less labour power is required.

This is something that all capitalists MUST DO if they are to survive, they are driven to constantly 'update' their technology - as charlie boy put it:

"accumulate accumulate...reconvert the hgreatest proportion of surplus value into capital. Accumulation for accumulations sake, production for productions sake".

Thus, capitalism is defined centrally by the need, according to an external iron law. it si competition between different poles of capitalism (which can be individual companies, or individual states, a la the USSR) that make them follow such laws, but that is only a factor, rather than the central dynamic & individual feature.
It is handy to try and say that capitalism is 'simply' competition tho, as that makes it appear far more as if it is an eternal presence, that cannot be changed.