Second, one may think about constructing more stringent tests, according to the following intuition. After all, if types in e(m) cannot gain by sending the message m, then the Receiver should take this into account; this much is incorporated in the above alternative formalization of the Intuitive Criterion test, but not in the definition of R(m Thus. we can iterate our definitions Fe(n)=BB((m),m),(m)={∈m0):m(m and so on(what would be the third step? This leads to the Iterated Intuitive Crite D1, D2, Divinity and friends his material goes beyond what we covered in class, but i thought you might find it Useful. Check Cho and Kreps's original paper for further info The Intuitive Criterion is not a panache, however. Consider once again the game of Figure 1, but change the payoffs by letting u1(Q, N, w)=2. Then the IC does not eliminate the(Q, Q, FN)equilibrium, because ui(w)=2= maxrERI u(m, r,w) However, consider the following argument The Weak Sender never gains by sending the message B. Also, the only case in which she is indifferent is when the Receiver responds with n On the other hand, if the Receiver responds to B with N, the Strong Sender gains by deviating In other words, for any response that makes the Weak Sender indiffer ent between deviating and playing as per the candidate equilibrium, the Strong Sender has a positive incentive to deviate. This suggests that the latter should be more likely to be the deviator This idea leads to a class of refinements known as D1, D2 and Divinity. First fixing a candidate equilibrium as above, for any type 0 Ee and out-of-equilibrium message m, define the set of mired responses of the Receiver that provide type 0 with a strict incentive to deviate to m as D(m)={y∈MBR2(O,m):1()<a1(m,r,0)y(r)} r∈R where MBR2(e, M) is defined analogously to BR2(0, M) (note that the former is not the convex hull of the latter-think about it! ) Also, define the set of mixed responsesSecond, one may think about constructing more stringent tests, according to the following intuition. After all, if types in Θ¯ 1 (m) cannot gain by sending the message m, then the Receiver should take this into account; this much is incorporated in the above alternative formalization of the Intuitive Criterion test, but not in the definition of R1 (m). Thus, we can iterate our definitions: R 2 (m) = BR2(Θ\Θ¯ 1 (m), m), Θ¯ 2 (m) = {θ ∈ Θ\Θ¯ 1 (m) : u ∗ 1 (θ) > max r∈R2(m) u1(m, r, θ)} and so on (what would be the third step?) This leads to the Iterated Intuitive Crite￾rion. D1, D2, Divinity and Friends [This material goes beyond what we covered in class, but I thought you might find it useful. Check Cho and Kreps’s original paper for further info.] The Intuitive Criterion is not a panache, however. Consider once again the game of Figure 1, but change the payoffs by letting u1(Q,N,w) = 2. Then the IC does not eliminate the (Q, Q, FN) equilibrium, because u ∗ 1 (w) = 2 = maxr∈R1 u 1 (m, r,w). However, consider the following argument. The Weak Sender never gains by sending the message B. Also, the only case in which she is indifferent is when the Receiver responds with N. On the other hand, if the Receiver responds to B with N, the Strong Sender gains by deviating. In other words, for any response that makes the Weak Sender indiffer￾ent between deviating and playing as per the candidate equilibrium, the Strong Sender has a positive incentive to deviate. This suggests that the latter should be more likely to be the deviator. This idea leads to a class of refinements known as D1, D2 and Divinity. First, fixing a candidate equilibrium as above, for any type θ ∈ Θ and out-of-equilibrium message m, define the set of mixed responses of the Receiver that provide type θ with a strict incentive to deviate to m as Dθ(m) = {ϕ ∈ MBR2(Θ, m) : u ∗ 1 (θ) < X r∈R u1(m, r, θ)ϕ(r)} where MBR2(Θ, M) is defined analogously to BR2(Θ, M) (note that the former is not the convex hull of the latter—think about it!) Also, define the set of mixed responses 5