strategies: it should be obvious to you that this makes no difference whatsoever in terms of outcomes. In practice, I collapse strategies such as OBB and OTB into a single reduced-form strategy 0B LL LR RL RR rT3-x,13-x,1-x,0 B|-x0 r,01-x,31-x,3 0T3,1 0.0 3,1 0,0 OB0.0 1,3 Figure 3: Burning Money in Normal Form Iterated Weak Dominance eliminates B, then RL and RR, then oB, then LR and finally T. Thus, it seems like IWD tracks the forward induction argument closely However, let us ask why this is the case. Look at RL and LL; once B is eliminated RL and RR are weakly dominated by LL and LR respectively. In particular, RL is weakly dominated by LL because it yields the same payoff as the latter strategy if chooses ot or OB, but a worse payoff if 1 chooses aT; note that aB has been ruled In other words, weak dominance captures sequential rationality: under the as- sumption that 1 follows a with T, R is not sequentially rational after a Very loosely speaking, we can expect IWD to"capture Fr'whenever weak domi- nance and sequential rationality coincide(perhaps given certain restrictions on belief as is the case here. But this is certainly not a general fact: think about any normal- form game, and a strategy in that game that is weakly but not strictly dominated You will also hear sometimes that "IWD captures backward induction. " This is even more confusing! The exact relationship between IWD, Bi and a version of FI (see below)is stated in Battigalli's 1997 paper on extensive-form rationalizability As far as I am concerned, this is what you need to know: IWD is a normal-form idea. It happens to induce the "right"(BI or FI)outcome sometimes, but essentially for technical reasons only. If you like weak dominance, that's fine, as long as your preference is motivated by entirely normal-form considerations. In my opinion, there is no compelling and general extensive-form reason to like weak dominance, and hence IWD Extensive-Form Rationalizability I did not cover this material in class, but I thought you might like to look at it anyway In particular, please look at the discussion of weak and full sequential rationality. A(much) better way to capture forward-induction reasoning is provided by ectensive- form rationalizability(EFR henceforth; cf. Pearce(1984); Battigalli (1996, 1997).)strategies: it should be obvious to you that this makes no difference whatsoever in terms of outcomes. In practice, I collapse strategies such as 0BB and 0TB into a single reduced-form strategy 0B. LL LR RL RR xT 3 − x, 1 3 − x,1 −x,0 −x,0 xB −x,0 −x,0 1 − x,3 1 − x,3 0T 3,1 0,0 3,1 0,0 0B 0,0 1,3 0,0 1,3 Figure 3: Burning Money in Normal Form Iterated Weak Dominance eliminates xB, then RL and RR, then 0B, then LR and finally xT. Thus, it seems like IWD tracks the forward induction argument closely. However, let us ask why this is the case. Look at RL and LL; once xB is eliminated, RL and RR are weakly dominated by LL and LR respectively. In particular, RL is weakly dominated by LL because it yields the same payoff as the latter strategy if 1 chooses 0T or 0B, but a worse payoff if 1 chooses xT; note that xB has been ruled out. In other words, weak dominance captures sequential rationality: under the as￾sumption that 1 follows x with T, R is not sequentially rational after x. Very loosely speaking, we can expect IWD to “capture FI” whenever weak domi￾nance and sequential rationality coincide (perhaps given certain restrictions on beliefs, as is the case here.) But this is certainly not a general fact: think about any normal￾form game, and a strategy in that game that is weakly but not strictly dominated. You will also hear sometimes that “IWD captures backward induction.” This is even more confusing! The exact relationship between IWD, BI and a version of FI (see below) is stated in Battigalli’s 1997 paper on extensive-form rationalizability. As far as I am concerned, this is what you need to know: IWD is a normal-form idea. It happens to induce the “right” (BI or FI) outcome sometimes, but essentially for technical reasons only. If you like weak dominance, that’s fine, as long as your preference is motivated by entirely normal-form considerations. In my opinion, there is no compelling and general extensive-form reason to like weak dominance, and hence IWD. Extensive-Form Rationalizability [I did not cover this material in class, but I thought you might like to look at it anyway. In particular, please look at the discussion of weak and full sequential rationality.] A (much) better way to capture forward-induction reasoning is provided by extensive￾form rationalizability (EFR henceforth; cf. Pearce (1984); Battigalli (1996, 1997).) 5