announced, it cheats any trader who offers to trade. Traders offer to trade in a given period if and only if no embargo has been announced.29
The formal proof is by direct verification. Condition 4 implies that what the city stands to gain by cheating a trader, which is proportional to cf(x*), is less than the average future profits from each trader, which is @(t!c)f(x*). With group enforcement, average trading profits rather than marginal profits determine the city's incentives. This accounts for the continued effectiveness of group sanctions even at the efficient level of trade.
In the institution captured in this equilibrium analysis, the city’s behavior is motivated by the beliefs that abuse will lead to an embargo while respecting rights after an embargo is announced will not cause the resumption of trade. The expectation that their rights will be respected motivates traders to trade; the expectation of being abused motivates them not to trade after an embargo is announced. As these beliefs are commonly known, each side takes the other side’s expected behavior as given, and each merchant and the city find it optimal to act as expected of them.
The equilibrium strategies contain a counterintuitive element: the city cheats any trader who offers to trade during an embargo. Traders' unanimous expectations that the city will behave this way cause all of them to honor the embargo. But why should the city not welcome traders during the embargo rather than cheat them? In a Markov perfect equilibrium, the city can be expected to cheat embargo-breaking traders only if it is in the city's interest to do so once the embargo has been announced. Given the specified strategies, if y traders violate the embargo and offer their goods, the city expects a payoff of (t!c)f(y) in the current period and zero in future periods if it acts honestly. If it cheats, it expects tf(y) in the current period and zero in the future. Cheating is therefore optimal.
Although the strategies described in proposition 4.3 constitute an equilibrium, the expectations and behavior that they entail seem implausible. The equilibrium requires, for example, that, no matter how desperate the city may be for renewed trade relationships, once an