This is a valid point. However, note that even generic games need not have pure-action equilibria(generic variants of Matching Pennies prove this point ). And, even taking the mixed extension of a finite game seriously, no mixed-action equilibrium can be strict(why? Hence,for games which admit equilibria only in their mixed representation,one really needs the full force of the non-decision-theoretic "correct beliefs "assumption The learning approach, by and large takes the point of view that players know how to st-respond to a belief, but it postulates that beliefs are based on the players experience from past strategic interactions The simplest such model is that of fictitious play. Each player i E N is endowed with a weighting function"w'i: A-i-10, 1, 2... which counts how many times a certain action profile was observed. Before playing the game, some arbitrary weights are assigned, and upon completing each play of the game, if a-i E A-i was observed, wi(a-i) is increased by 1. Finally, at each stage players best-respond to the belief a i defined by -i)= i.e. they play some action in riai The attractiveness of this approach lies in the intuitive notion that perhaps learning might be the reason why beliefs are correct. That is, intuitively players might learn how to coordinate"on some Nash equilibrium Indeed, several results relate the steady states of this process, or the long-run frequencies, i.e. the long-run ais, to Nash equilibrium and other solution concepts. For instance, it can be shown that, in two-player games, if a steady state exists, it must be a strict Nash equilibrium (this is not hard to prove). Also, if the long-run frequencies converge, they represent equilibria of the mixed extension of the game under consideration The above paragraphs are simply meant to convey the flavor of the learning approach: I am certainly not doing any justice to the vast and insightful literature on the subject Scant as they are, however, the above remarks do illustrate at least one difficulty in applying the ideas from the learning literature to justify Nash equilibrium: convergence to a steady state, or convergence of the long-run frequencies, is not guaranteed at all: it only occurs under appropriate conditions. Indeed, most of these conditions are either very restrictive, or sufficient to enable a fully decision-theoretic eductive analysis, without invoking the full strength of the "correct beliefs" assumption The recent learning literature uses this approach not to justify existing solution concepts but to provide a foundation for new, interesting ones(e. g. Fudenberg and Levine's self- confirming equilibrium) which typically involve departures from "correct beliefs 3Fudenberg and Levine's book is an excellent reference, if you are interestedThis is a valid point. However, note that even generic games need not have pure-action equilibria (generic variants of Matching Pennies prove this point). And, even taking the mixed extension of a finite game seriously, no mixed-action equilibrium can be strict (why?). Hence, for games which admit equilibria only in their mixed representation, one really needs the full force of the non-decision-theoretic “correct beliefs” assumption. The learning approach, by and large, takes the point of view that players know how to best-respond to a belief, but it postulates that beliefs are based on the players’ experience from past strategic interactions. The simplest such model is that of fictitious play. Each player i ∈ N is endowed with a “weighting function” wi : A−i → {0, 1, 2 . . .} which counts how many times a certain action profile was observed. Before playing the game, some arbitrary weights are assigned, and upon completing each play of the game, if a−i ∈ A−i was observed, wi(a−i) is increased by 1. Finally, at each stage players best-respond to the belief α w −i defined by α w −i (a−i) = wi(a−i) P a 0 −i∈A−i wi(a−i) i.e. they play some action in ri(α w −i ). The attractiveness of this approach lies in the intuitive notion that perhaps learning might be the reason why beliefs are correct. That is, intuitively players might learn how to “coordinate” on some Nash equilibrium. Indeed, several results relate the steady states of this process, or the long-run frequencies, i.e. the long-run α w −i ’s, to Nash equilibrium and other solution concepts. For instance, it can be shown that, in two-player games, if a steady state exists, it must be a strict Nash equilibrium (this is not hard to prove). Also, if the long-run frequencies converge, they represent equilibria of the mixed extension of the game under consideration. The above paragraphs are simply meant to convey the flavor of the learning approach: I am certainly not doing any justice to the vast and insightful literature on the subject3 . Scant as they are, however, the above remarks do illustrate at least one difficulty in applying the ideas from the learning literature to justify Nash equilibrium: convergence to a steady state, or convergence of the long-run frequencies, is not guaranteed at all: it only occurs under appropriate conditions. Indeed, most of these conditions are either very restrictive, or sufficient to enable a fully decision-theoretic eductive analysis, without invoking the full strength of the “correct beliefs” assumption. The recent learning literature uses this approach not to justify existing solution concepts, but to provide a foundation for new, interesting ones (e.g. Fudenberg and Levine’s self￾confirming equilibrium) which typically involve departures from “correct beliefs.” 3Fudenberg and Levine’s book is an excellent reference, if you are interested. 7