that the Sender is rational However, in this game u1(B, N, w)=2, so B is not strictly dominated by Q for the Weak Sender. For instance, if the Sender expects the Receiver to play NF, contrary to the equilibrium prescription, then it's perfectly OK for her to choose B Still, a slightly modified version of the dominance idea works here. One way to motivate it is to note that, if we want to take the notion of equilibrium at least a little seriously, we should not allow the Weak Sender to expect the receiver to play anything other than what the equilibrium prescribes, as long as no deviation has occurred. In particular, the Weak Sender should believe that the Receiver will respond to Q with N Note well that we do not need to assume that the Receiver will respond to the out-of-equilibrium message B with F, as prescribed by the equilibrium. After all, the whole point is that we are not so sure this response is reasonable! What we do wish to maintain, though, is the assumption that, on the equilibrium path, players behave as prescribed by the equilibrium But this suffices to eliminate b for the Weak Sender Why should the Weak Sender choose a message which, even under the most optimistic circumstances (i.e. even if the Receiver responds with N B), leaves her with a payoff of 2, which is strictly less than what she gets in equilibrium? On the other hand, the Strong Sender is getting 2 in quilibrium, and if the Receiver was convinced that only a Strong Sender might choose B, she could potentially get a payoff of 3 To sum up, the Weak Sender can only lose(compared with the equilib- rium outcome) by sending B, whereas the Strong Sender has a positive incentive to send B (relative to the equilibrium outcome. But the out- of-equilibrium beliefs necessary to support( Q, Q, FN) do not reflect this so the equilibrium is unreasonable The Intuitive Criterion formalizes these intuitions, with an additional twist. Sup- pose that, following each message, the Receiver had another response available-to donate $10,000 out of his own pockets to the Sender. Then the preceding argument would not work, because even the Weak Sender might have an incentive to deviate to B-if she somehow expected the Receiver to donate $10,000 to her We cannot accept this as a reasonable justification for the choice of B: after all donating $10,000 is(conditionally) strictly dominated for the Receiver, i. e. it is never a best response. Thus, we restrict the beliefs of the Weak Sender to best replies of the receiver, and the argument goes through as before. The resulting test is called equilibrium domination, for obvious reasonsthat the Sender is rational. However, in this game u1(B,N,w) = 2, so B is not strictly dominated by Q for the Weak Sender. For instance, if the Sender expects the Receiver to play NF, contrary to the equilibrium prescription, then it’s perfectly OK for her to choose B. Still, a slightly modified version of the dominance idea works here. One way to motivate it is to note that, if we want to take the notion of equilibrium at least a little seriously, we should not allow the Weak Sender to expect the Receiver to play anything other than what the equilibrium prescribes, as long as no deviation has occurred. In particular, the Weak Sender should believe that the Receiver will respond to Q with N. Note well that we do not need to assume that the Receiver will respond to the out-of-equilibrium message B with F, as prescribed by the equilibrium. After all, the whole point is that we are not so sure this response is reasonable! What we do wish to maintain, though, is the assumption that, on the equilibrium path, players behave as prescribed by the equilibrium. But this suffices to eliminate B for the Weak Sender: Why should the Weak Sender choose a message which, even under the most optimistic circumstances (i.e. even if the Receiver responds with N to B), leaves her with a payoff of 2, which is strictly less than what she gets in equilibrium? On the other hand, the Strong Sender is getting 2 in equilibrium, and if the Receiver was convinced that only a Strong Sender might choose B, she could potentially get a payoff of 3. To sum up, the Weak Sender can only lose (compared with the equilib￾rium outcome) by sending B, whereas the Strong Sender has a positive incentive to send B (relative to the equilibrium outcome.) But the out￾of-equilibrium beliefs necessary to support (Q, Q, FN) do not reflect this, so the equilibrium is unreasonable. The Intuitive Criterion formalizes these intuitions, with an additional twist. Sup￾pose that, following each message, the Receiver had another response available—to donate $10,000 out of his own pockets to the Sender. Then the preceding argument would not work, because even the Weak Sender might have an incentive to deviate to B—if she somehow expected the Receiver to donate $10,000 to her. We cannot accept this as a reasonable justification for the choice of B: after all, donating $10,000 is (conditionally) strictly dominated for the Receiver, i.e. it is never a best response. Thus, we restrict the beliefs of the Weak Sender to best replies of the Receiver, and the argument goes through as before. The resulting test is called equilibrium domination, for obvious reasons. 3