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Answer:
Consider the following explanation
Explanation:
Answer to Q (a)
Players: Citizens 1 and 2 along with States {A, B}.
Actions:
The set of actions of each player is {0, 1, 2} (where 0 means do not vote).
Signals:
Citizen 1 receives different signals in states A and B, whereas citizen 2 receives the same signal in both states.
Beliefs:
Each type of citizen 1 assigns probability 1 to the single state consistent with her signal.
The single type of citizen 2 assigns probability 0.9 to state A and probability 0.1 to state B.
Payoffs:
Both citizens Bernoulli payoffs are 1 if either the state is A and candidate 1 receives the most votes or the state is B and candidate 2 receives the most votes;
Their payoffs are 0 if either the state is B and candidate 1 receives the most votes or the state is A and candidate 2 receives the most votes;
Otherwise their payoffs are ½
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Answer to (b)
State A of citizen 1’s best action depends only on the action of citizen 2;
=> To vote for candidate 1 if citizen 2 votes for candidate 2 or does not vote, and either to vote for candidate 1 or not vote if citizen 2 votes for candidate 1.
Similarly, for state B of citizen 1’s best action is to vote for candidate 2 if citizen 2 votes for candidate 1 or does not vote, and either to vote for candidate 2 or not vote if citizen 2 votes for candidate 2.
Citizen 2’s best action is to vote for candidate 1 if state A -> citizen 1 either does not vote or votes for candidate 2 (regardless of how state B -> citizen 1 votes), not to vote if state A of citizen 1 votes for candidate 1 and state B of citizen 1 either votes for candidate 2 or does not vote, and either to vote for candidate 1 or not to vote if both types of citizen 1 vote for candidate 1.
Given the best responses of the two types of citizen 1, their only possible equilibrium actions are
(0, 0) (I.e. both do not vote), (0, 2), (1, 0), and (1, 2).
Checking citizen 2’s best responses we see that the only equilibria are
(i)==> (0, 2, 1) (Citizen 1 does not vote in state A and votes for candidate 2 in state B; Citizen 2 votes for candidate 1)
(ii)==> (1, 2, 0) (Citizen 1 votes for candidate 1 in state A and for candidate 2 in state B; citizen 2 does not vote).
(ii)
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Answer to (c)
Swing Voter’s curse:
Swing voter is an important player whose decision can affect the result of the election. Swing voters curse results into equilibrium as shown below.
In the equilibrium (1, 2, 0), Citizen 2 does not vote. This is because if she votes, then in the only case in which her vote affects the outcome (i.e. the only case in which she is a swing voter), it affects it adversely as shown below:
i. If she votes for candidate 1 then her vote makes no difference in state A, whereas it causes a tie, instead of a win for candidate 2 in state B
ii. If she votes for candidate 2 then her vote causes a tie, instead of a win for candidate 1 in state A, and makes no difference in state B.
