For now, you've only illustrated with clear examples the thesis I stated from the beginning. That is, the relationships within compact human communities are quite reliably studied by archaeology, but the relationships between these communities are not very well studied.
I can't think of any other explanation for your persistent evasion of a rather simple and clear question.
Okay, then I'll try to reason it out myself. Let's take the simplest question to analyze – the regular payment of tribute from state A to state B. To confirm this, at least a large number of household items that are produced only in A must be found on the territory of B. Let's assume that such finds exist, that is, the flow of goods in one direction has been proven.
Now, we need to rule out the possibility of trade relations. To do this, goods characteristic of exports from B should not be found on the territory of A. Moreover, it is desirable that they are not found at all, since finding them in small quantities already suggests that there may have been many, but not all of them have survived.
But that's not enough, as export goods may be among those that do not survive in the ground. Or they may be some kind of services that cannot leave any traces in principle. Therefore, it is also desirable to show the presence of violent actions by B against A – traces of battles, mass burials, and обязательно with traces of weapons used by B's warriors (otherwise, it can be attributed to internal conflicts). Moreover, it is desirable to show the absence or minimal number of casualties among B's warriors.
Another possible factor is to show the prevalence of slavery of residents of A on the territory of B. That is, the factor of their presence there and low social status. And the absence of such finds from residents of B on the territory of A.
Am I reasoning correctly? Can you recall examples of A+B for which these or similar conditions are met?
For example, the first stage of the Spanish conquest of America. American gold items and vegetables, etc., appear in Spain, and in return, there are many corpses in America. And only later, not immediately, colonization begins, when Spanish goods (for example, slaves) appear in America, of course, for the needs of the Spanish.
The Opium War between Great Britain and the Qing Empire
Result:
"The result of the war was the victory of Great Britain, enshrined in the Treaty of Nanjing on August 29, 1842, the payment by the Qing Empire of a tribute of 15,000,000 silver taels ($21,000,000), the transfer of Hong Kong Island to Great Britain, and the opening of Chinese ports for English trade. The British Crown received a giant source of income by selling opium.
The First Opium War became the beginning of a long period of weakening of the state and civil unrest in the Qing Empire, which led to the subjugation of the country by European powers, as well as to the massive spread of drug addiction, the degradation, and mass extinction of the Chinese population. In 1842, the population of the empire was 416,118,200 people, of which 2 million were drug addicts; in 1881, it was 369,183,000 people, of which 120 million were drug addicts."
Interesting trade: exotic goods are supplied to England, and drug addicts are supplied to China. Even worse than tribute.