Monopoly on Violence
The key point here is 'monopoly on violence.' In the modern world, governments have a monopoly on violence. There are plenty of places where that is not true (South Sudan, Somalia, Syria, Libya, etc), but in general those places have either never had any sort of working modern economy (Somalia, South Sudan) or their modern economy has been completely wrecked by an all-out civil war (Syria, Libya).
What you want is a place where the government does not have a monopoly on violence, but there isn't an all-out civil war.
The most obvious comparison in the Middle Ages. There was no government monopoly on violence and many minor lords entertains squabbles and feuds that broke out into low grade warfare. They were enabled to do this by their fortifications, which made it too costly for a king with a superior army to defeat them (after all, sieges cost a lot of money). Another apt comparison was the 'Wild West' and its equivalent in the Russian expansion through Siberia. In those places, people just came and went as they pleased and distance made establishing state control difficult. In order to control violence on a local level, people had to band together in 'corporations' (of cattlemen, brigands, sherrif's posses, etc) to deter violence. Two 'corporations' meeting in that context was basically the showdown at the OK Corral.
So to get a similar scenario, you have to have a world where there is limited government oversight and difficulty in enforcing claims of violence monopoly on the corporations either due to a. the corporation's ability to withstand a siege from government forces or b. the distance from government control.
If either criteria is met, then you can expect corporations to act just like feudal barons and Western gangs.