Definitions

First we need to clarify some terms:

• Capitalism — An economic system that's based primarily on free-market competition, and reduces the emphasis of central planning or any other form of government intevention or regulation. This specific form of competition only goes back to the Middle Ages.
• Economic competition — Any time that two or more actors compete to sell goods/services at a lower price. There are many economic systems that have some form of competition mixed with central planning, so economic competition existed much further back in history.
• Market — An ecosystem of people who are competing. "Competition" can involve only two people, "market" implies a larger number of people being involved.

But even that is too skewed towards a modern perspective. "Competition" and "markets" don't have to involve money:

• Buying/selling — exchanging goods/services for money.

• Bartering — directly exchanging one good/service for another good/service, without an intermediate currency.

Early examples of markets

• Street markets — food stalls where vendors sell their fresh wares. This has occured since the beginning of agriculture.
• Bazaar — a permanent location for a street market, often with fixed buildings.
• Tax farming — began with the Romans, and involved wealthy individuals bidding (competing) to pay higher collective taxes for a single area/region.