That's not entirely true.  Two parties may resolve a dispute themselves. IF they believe that it is less costly than a physical confrontation.  Anarcho-capitalists also theorize that third party mediators will offer their services in dispute resolution based on commonly-accepted community norms. If Both parties can agree on a third party Dispute Resolution Organization, then they would also have to agree on mechanisms for enforcing the outcome.

War is expensive. Throughout history, you will find that it is mostly engaged in by parties that do not bear the full cost. We propose that any parties engaging in physical conflict bear the full cost of doing so, thereby discouraging the practice. 

Reputation also has an economic and social value. Credit scores are one example.  Other members of the community can enforce laws and contracts even if they are not a direct party by imposing opportunity costs on violators. An example: you defaulted on a loan, so most others will refuse to lend to you in the future, and if they do it will be at a much higher interest rate.  or another: You punch somebody in the nose and word gets out so you are no longer welcome at certain social events.