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4. (30 points) Consider the following two-player game, played between a think tank (Sender) and a policy- maker (Receiver). The policymaker decides between two reforms
4. (30 points) Consider the following two-player game, played between a think tank (Sender) and a policy- maker (Receiver). The policymaker decides between two reforms and a status quo. The think tank knows which of two reforms is better than the other for the policymaker. The think tank wants a reform rather than the status quo, but has a political agenda and so strictly prefers one reform. The think tank would choose a reform if it is known to be the better one, but would prefer the status quo if sufficiently uncertain. Play proceeds as follows: N . First, Sender learns her type t E {(, r), where both types are equally likely. . Then, Sender conveys a cheap talk message in { left, right}. . Having heard the message, Receiver chooses an action y E {L, S, R}. Payoffs are as follows: : (y, t) = (L, () or (y, t) = (R, r) up ( y, t ) = 3 - 2 : (y, t ) = (L, r) or (y, t) = (R, e) :(y, t) = (S, () or (y, t) = (S, r) 0 :y= S u' ( y, t ) = 1 : y = L 2 : y = R. (a) What payoffs can Sender get in an equilibrium in which Receiver uses a pure strategy? (b) What payoffs can Sender get in an equilibrium in which Sender uses a pure strategy? (c) Construct an equilibrium in which Sender gets a strictly positive payoff
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