Proposition 4.2: No Nash equilibrium of game 2 can support honest trade (Dt / 0) at the efficient level (xt / x*), regardless of the levels of c, t, T, or B.
The proof is essentially the same as for the first proposition, except that the bound on the number of traders who decline to trade in the future is multiplied by K. Expression (3) is replaced by cf(x*) ! @K(t!c)x*fN(x*) = cf(x*) > 0.
Violations against a few merchants that are noticed only by proportionally few merchants cannot be deterred by a threat of retaliation by those with first hand knowledge.
The real situation faced by traders is considerably more complicated than that modeled in games 1 and 2. One important missing element concerns informal and word-of-mouth communication. Although game 2 allows that some traders are informed when the city cheats any trader, it also assumes that traders know nothing about who else is currently trading. This assumption is a device to rule out endogenous communication among the traders in the game, by which one trader may infer that another was cheated because he did not show up to trade. In theory, this kind of communication can be significant (Kandori 1992). Both word-of-mouth communication and some inferences of this kind could take place, but the model disallows them on the assumption that they were of minor importance for enforcing contract compliance. To the extent that informal communications and indirect inferences could provide effective information, the need for organized communication and coordination is reduced.
Game 3: Guild Organization with Coordinating Ability. We have seen that it is impossible for the city and traders to sustain an efficient level of trade based only on sanctions applied by small groups. Given the historical evidence of the existence of organizations that governed the relationships between traders and the city, it is natural to examine whether these could contribute to trade expansion. If these organizations, as conjectured here, linked information sharing transactions among all merchants, could they have supported the efficient level of trade? Could they have rendered self-enforcing the beliefs that no right will be abused in the efficient level of trade?
A crucial characteristic that separates formal organizations such as guilds from informal codes of behavior is the creation of specialized roles (positions), such as those of the guild's