%s There is little reason why this concept should not apply to general extensive games well. However, observe that, in games with observed actions, fixing a strategy profile s is sufficient to generate well-defined beliefs in every subgame-i e. well-defined beliefs conditional upon reaching any history. This is not the case in general extensive games(or in Bayesian extensive games with observed actions, for that matter) In some(very special)games, this does not really matter. For instance, consider Fig. 1 0.0 Figure 1: A special game(OR 219.1) Observe that (L, r)is a Nash equilibrium of this game; note also that, since Player 1 chooses L in this equilibrium, it is not clear what Player 2 should believe if the information set I2=I(M), (R)) is reached! Thus, the equilibrium strategy profile is insufficient to pin down players' conditional beliefs Yet, in this particular game, this is essentially irrelevant: regardless of his beliefs about Player 1s actual choice, r is conditionally strictly dominated at 12. Whatever Player 2s beliefs, r cannot thus be sequentially rational, So(L, r)is "not a legitimate solution"to the extensive game in Figure 1. On the other hand, (M, I)is In this simple game, Player 2's beliefs about the strategy(action) actually chosen by Player 1 is irrelevant as far as his choices are concerned. However, this is seldom the case consider Fig. 2, which differs from Fig. 1 only in that the payoffs at the terminal history IM, r have been modified Consider (L, r) again. Upon being reached, Player 2 must conclude that Player 1 did not choose L; hence, he must adopt new, distinct from the equilibrium profile. Suppose that he thinks that Player 1 actually chose M: then r is indeed a sequential best reply! Suppose instead that he thinks that Player 1 chose R: in this case r is not sequentially rationalThere is little reason why this concept should not apply to general extensive games as well. However, observe that, in games with observed actions, fixing a strategy profile s is sufficient to generate well-defined beliefs in every subgame—i.e. well-defined beliefs conditional upon reaching any history. This is not the case in general extensive games (or in Bayesian extensive games with observed actions, for that matter). In some (very special) games, this does not really matter. For instance, consider Fig. 1. L 2,2 1 q M ￾ ￾ ￾ ￾￾ R ❅ ❅ ❅ ❅ q ❅ r ❆ ❆ ❆ ❆ ❆ 0,0 l ✁ ✁ ✁ ✁ ✁ 3,1 q 1,1 ❆ ❆ ❆ ❆ ❆ 0,2 ✁ ✁ ✁ ✁ ✁ 2 I2 Figure 1: A special game (OR 219.1) Observe that (L, r) is a Nash equilibrium of this game; note also that, since Player 1 chooses L in this equilibrium, it is not clear what Player 2 should believe if the information set I2 = {(M),(R)} is reached! Thus, the equilibrium strategy profile is insufficient to pin down players’ conditional beliefs. Yet, in this particular game, this is essentially irrelevant: regardless of his beliefs about Player 1’s actual choice, r is conditionally strictly dominated at I2. Whatever Player 2’s beliefs, r cannot thus be sequentially rational, so (L, r) is “not a legitimate solution” to the extensive game in Figure 1. On the other hand, (M, l) is. In this simple game, Player 2’s beliefs about the strategy (action) actually chosen by Player 1 is irrelevant as far as his choices are concerned. However, this is seldom the case: consider Fig. 2, which differs from Fig. 1 only in that the payoffs at the terminal history {M, r} have been modified. Consider (L, r) again. Upon being reached, Player 2 must conclude that Player 1 did not choose L; hence, he must adopt new, distinct from the equilibrium profile. Suppose that he thinks that Player 1 actually chose M: then r is indeed a sequential best reply! Suppose instead that he thinks that Player 1 chose R: in this case r is not sequentially rational. 2