(a) Draw the game in extensive form specifying who moves when, the set of actions available at each node, the final payoffs to both players (clearly denote information sets). (b) Is there an equilibrium where the M-state always acquiesces when there is a protest, the H-state always represses when there is a protest and society always protests unless it has been repressed in period 1 in which case she stays home in period 2? If an equilibrium exists, what values of p0 does it hold for? (c) Is there an equilibrium where both types of states repress in period 1 when there is a protest, the M-state acquiesces in period 2 after a protest, the H-state represses in period 2 after a protest and society always protests unless it has been repressed in period 1 in which case she stays home in period 2? If an equilibrium exists, what values of p0 does it hold for? (d) Is there an equilibrium where both types of states repress in period 1 when there is a protest, the M-state acquiesces in period 2 after a protest, the H-state represses in period 2 after a protest and society always stays home? If an equilibrium exists, what values of p0 does it hold for?
Suppose that in each of two periods, society must decide whether to protest the policies of the state. When society protests, the state may either acquiesce or repress. Society gets 1 if the state acquiesces, -1 if the state represses, and 0 if it does not protest.
Suppose there are two types of states: Moderate and Hardline. The moderate state (M) gets 0 if the protest does not take place, -2 if it acquiesces, and -3 if it represses. The hardline (H) state gets 0 for no protest, -2 for repression, and -3 for acquiescing. Let p0 be the prior probability the state is M. Let p1 be society’s updated belief that the state is M, after observing the actions in period 1.
(a) Draw the game in extensive form specifying who moves when, the set of actions available at each node, the final payoffs to both players (clearly denote information sets).
(b) Is there an equilibrium where the M-state always acquiesces when there is a protest, the H-state always represses when there is a protest and society always protests unless it has been repressed in period 1 in which case she stays home in period 2? If an equilibrium exists, what values of p0 does it hold for?
(c) Is there an equilibrium where both types of states repress in period 1 when there is a protest, the M-state acquiesces in period 2 after a protest, the H-state represses in period 2 after a protest and society always protests unless it has been repressed in period 1 in which case she stays home in period 2? If an equilibrium exists, what values of p0 does it hold for?
(d) Is there an equilibrium where both types of states repress in period 1 when there is a protest, the M-state acquiesces in period 2 after a protest, the H-state represses in period 2 after a protest and society always stays home? If an equilibrium exists, what values of p0 does it hold for?
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