Thus, it seems that, if we wish to invoke the notion of Nash equilibrium to draw behavioral predictions, i.e. to say what players will in fact do, we are forced to accept the full force of the "correct beliefs"assumption. As I have observed, this assumption might be unpalatable. and does not add much to our understanding of the formal definition Mixed actions I will be more concise with respect to the possibility of randomization. There is no doubt that mixing was introduced merely as a matter of technical convenie This is not to deny that, in many situations(e.g. the game of Rock, Scissors, Paper, or my own personal favorite, Matching Pennies), randomization is an appealing option Rather, this is to say that, when we represent Matching Pennies as we conventionally do(each player has two actions, H and T), we are really writing down an incomplete repre- sentation of the actual situation. Perhaps I would not go so far as to say that players can randomize with any probability between H and T, but I would not feel bad about assuming that, for instance, they can Hip a coin and choose an action based on the outcome of the coin toss Thus, if we feel that randomization is an important strategic option, then perhaps it ight be more appropriate to model it explicitly An alternative exists, however. We can interpret mixed strategies as beliefs held by the players about each other Under this interpretation, to say that(a1, a2) is a Nash equilibrium is to say that a1 ewed as a belief held by Player 2 about Player 1, is a belief which satisfies two consistency conditions Player 2 believes that Player 1 is rational (2)Player 2 believes that Player 1s beliefs are given by 2 Similar considerations hold for a2, viewed as a belief held by Player 1 about Player 2 Again, the details will only be clear once we have a full-blown model of interactive beliefs (note that(2) is not an assumption we know how to formulate yet); however, observe that(1) and(2) are statements that have to do with beliefs, not with behavior. They are, so to speak purely decision-theoretic statements-although they have no direct behavioral implication and adding the assumption that players are indeed rational may lead to the difficulties highlighted above with reference to the game in Figure In practice, a player may physically generate a sequence of coin tosses prior to playing the game, then memorize it and use it to choose an action each time she has to play 8Thus, it seems that, if we wish to invoke the notion of Nash equilibrium to draw behavioral predictions, i.e. to say what players will in fact do, we are forced to accept the full force of the “correct beliefs” assumption. As I have observed, this assumption might be unpalatable, and does not add much to our understanding of the formal definition. Mixed actions I will be more concise with respect to the possibility of randomization. There is no doubt that mixing was introduced merely as a matter of technical convenience. This is not to deny that, in many situations (e.g. the game of Rock, Scissors, Paper, or my own personal favorite, Matching Pennies), randomization is an appealing option. Rather, this is to say that, when we represent Matching Pennies as we conventionally do (each player has two actions, H and T), we are really writing down an incomplete repre￾sentation of the actual situation. Perhaps I would not go so far as to say that players can randomize with any probability between H and T, but I would not feel bad about assuming that, for instance, they can flip a coin and choose an action based on the outcome of the coin toss.4 Thus, if we feel that randomization is an important strategic option, then perhaps it might be more appropriate to model it explicitly. An alternative exists, however. We can interpret mixed strategies as beliefs held by the players about each other. Under this interpretation, to say that (α1, α2) is a Nash equilibrium is to say that α1, viewed as a belief held by Player 2 about Player 1, is a belief which satisfies two consistency conditions: (1) Player 2 believes that Player 1 is rational (2) Player 2 believes that Player 1’s beliefs are given by α2 Similar considerations hold for α2, viewed as a belief held by Player 1 about Player 2. Again, the details will only be clear once we have a full-blown model of interactive beliefs (note that (2) is not an assumption we know how to formulate yet); however, observe that (1) and (2) are statements that have to do with beliefs, not with behavior. They are, so to speak, purely decision-theoretic statements—although they have no direct behavioral implication, and adding the assumption that players are indeed rational may lead to the difficulties highlighted above with reference to the game in Figure 1. 4 In practice, a player may physically generate a sequence of coin tosses prior to playing the game, then memorize it and use it to choose an action each time she has to play. 8