destruction of goods and loss of value. Whatever the merchants were willing to pay the ruler—that is, all issues of transfer—are modeled here as part of the tax.
Game 1: Informationally Isolated Traders: Bilateral Reputation Mechanism. The first model represents the situation of merchants who travel alone or in small groups with no social or economic organization. The traders remain unaware of how the city has treated other merchants. Only intertemporal linkages between each ruler-merchant transaction are considered. Although this model is surely too extreme to be fully descriptive, it highlights the difficulties faced by individual merchants negotiating with the city on their own but able to condition their future transactions on past conduct.
In this game, knowing only the history of his own decisions and his own past treatment by the city, a trader must decide whether to bring his goods to the city in each period. A strategy for the trader is a sequence of functions mapping this history into decisions about whether to offer his goods for trade in that period. Similarly, the city must decide the property of which traders to abuse under various conditions. A strategy for the city is a sequence of functions identifying a (measurable) subset of the current traders for the city to abuse as a function of who shows up to trade currently and the full past history of the game.
Readers familiar with either the economics of reputations or the theory of repeated games will recognize that the repetition of the interactions between the city and the individual traders creates the possibility for reputations to be created that enforce good behavior by the city. The idea is that a trader who is abused once might refuse to return to the city, reducing the city’s profits. The effectiveness of this threat depends on both the frequency of trade and the periodic value of the individual merchant's trade in the city. If the frequency of trade is sufficiently high and the volume sufficiently low so that the value of the repeat business of any individual trader to the city is high, the simple reputation mechanism can be effective in providing the city with incentives to protect individual rights. In the analysis, however, when the volume of trade rises to the efficient level the value of repeat business falls to zero, so the usual conclusions of the Folk theorem of repeated games do not apply at the efficient level.