The Myerson Model Discussion

Question Description

I’m working on a economics test / quiz prep and need an explanation and answer to help me learn.

Recall the Myersons model (the model of weak institutions) discussed in Section 6. We did not discuss so much the effect of the leaders exogenous payoff ?? for surviving the second period. Assume pr < c 4c-2r. Complete the following sentence by choosing the appropriate words in (i) and (ii). If R increases, the leader is (i) more/less likely to survive without weak institutions, and the weak institutions becomes (ii) more/less important for the leader. Why is this statement obtained? Explain the reason based on the model.*Discussed Myerson’s model is attached as a doc.**Since I’m running out of time, you don’t have to answer all the (a), (b), and (c). You could only do one of them.

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Assume a polity consisting of an incumbent leader and two captains, with the later indexed by ?? =
??, ??. Over two periods, ?? = 1,2, the incumbent leader faces a challenge to their rule that can only
be faced with help from the captains. That is, there are two challengers, and one challenger fights
against the leader in each period. At the start of period 1and again in period 2 if the leader is
still in powereach captain decides whether to exert observable effort. Observable means that
the other players can witness whether the captain exerts effort or not, while exert effort means,
for instance, participation in the conflict and contributions to the costs of conflict. The leader
survives (to fight another day in the first period) with probability 1 if both captains exert effort, but
with probability ?? if only one does (0 < ?? < 1), and with probability zero if neither does. The value of ?? represents the leaders power, that is, the leaders ability to survive even when the leader has only partial support from the captains. Each captain bears a cost ?? > 0 for each period in which
they exert effort. In period 1, if the leader survives, the leader may (partially) compensate for these
costs by choosing a wage ???? ? 0 to provide each captain ?? in return for the effort by that captain.
Critically, we do not assume that the leader can credibly commit to this wage ex ante. Rather, in
equilibrium, it must be in the leaders self-interest to provide this wage after the captains have
decided whether to exert effort. Note that this wage might not be monetary compensation; it can
include sharing power, no taxation on investments, as well as organizational privileges and resources
for the military. Beyond the possible wage, each captain receives an exogenous payoff ?? > 0 if the
leader survives through the second period and the captain exerts effort in the second period. The
leader receives an exogenous payoff ?? > 0 for surviving the second period. To focus on the
interesting case, we assume that ???? < ?? < ?? < 2??. If the captain does not exert effort, they cannot get anything. If both captains exert effort, both can obtain ?? by paying the cost of effort ??. If the captain exerts effort but not the other, the probability that the leader survives ??, so the captains expected payoff is ???? ? ??. It is assumed that ???? < ?? < ??, which means that ?? ? ?? > 0 and ???? ? ??