People would find that the decisions of one court were prompter or easier to predict than those of another or that the customers of one protection agency were better protected than those of another. The protection agencies, trying to build their own reputations, would search for the 'best' courts. Several objections may be raised to such free-market courts. The first is that they would sell justice by deciding in favor of the highest bidder. But there can be two competing theories about the law of gravity or the proper definition of property rights.
Discovery is as much a productive activity as creation.
If it is obvious what the correct law is, what rules of human interaction follow from the nature of man, then all courts will agree, just as all architects agree about the laws of physics. If it is not obvious, the market will generate research intended to discover correct laws. Another objection is that a society of many different legal systems would be confusing. If this is found to be a serious problem, courts will have an economic incentive to adopt uniform law, just as paper companies have an incentive to produce standardized sizes of paper. New law will be introduced only when the innovator believes that its advantages outweigh the advantages of uniformity.