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Consider possible interactions between a strong and a weak enemy, when the strong takes the initiative. The strong enemy has the option to offend greatly
Consider possible interactions between a strong and a weak enemy, when the strong takes the initiative. The strong enemy has the option to offend greatly G, mildly M, or not N; in response, the weak enemy has the option to attack A (retaliate) or not N (ignore); and then the strong enemy, in its own response, can attack A or not N. In terms of welfare, the strong experiences much pleasure in seeing the weak unhappy, and much pain in seeing the weak happy. The strong suffers opprobrium from onlookers if it offends the weak, and especially if it attacks the weak without having been attacked. The weak suffers from being offended, and especially from being attacked. The weak must balance, in deciding whether to attack the strong in response to the strong's initial move, between preserving its honor and looking reasonable to onlookers; an attack in response to an offense defends its honor but is approved by onlookers only if the offense was great. The following extensive form game captures this situation: a. Concerned by onlookers' opprobrium of the strong's many past offenses and attacks, advisors to the strong advise it to greatly offend the weak, in the expectation that the weak would attack in response, and yield the strong an opportunity to be peaceful, impress onlookers, and avoid further opprobrium. Explain quantitatively and conceptually the one reason this is shoddy advice. b. Advisers to the strong try to improve the above advice so. They reason that now a mild offense is better than the original great offense, toward provoking an attack from the weak to yield the strong that opportunity at impressing onlookers as peaceful. After all, a mild offense carries less opprobrium than a strong offense, and opprobrium is precisely what the advisors seek to mitigate or reverse. Explain quantitatively and conceptually the two reasons this is shoddy advice. c. Describe the backward induction equilibrium path of play, i.e. the sequence of actions
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