On cycles in AS relationships

Why can the global Internet not have any AS relationship cycles? Why does it have to be a DAG (directed acyclic graph)? AS relationships emerge from business negotiations between pairs of ASs, while all relevant information is kept secret. In other words, local negotiations and interactions between AS pairs determine their relationships. Given the complexity of business agreements, it is quite unlikely that the local, independent, and diverse interactions between ASs yield a global, highly organized, and strictly hierarchical DAG structure.