Under what condition would the law of one price hold?
Converting my comments to an answer. The law of one price (LoP) is an economic concept which posits that "a good must sell for the same price in all locations". This law is derived from the assumption of the inevitable elimination of all arbitrage. Source wikipedia.

Arbitrage opportunities imply the law of one price but the reverse is not always true. In logic, LoP is a necessary condition for arbitrage but not a sufficient one. In common language, we cannot out rule out the fact that the law of one price may hold without full arbitrage. If the price of an asset is not different for different people, the law of one price holds without assuming full arbitrage.