An equilibrium cannot occur at a point not in the intersection of the two reaction curve1

An equilibrium cannot occur at a point not in the intersection of the two reaction curve1

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An equilibrium cannot occur at a point not in the intersection of the two reaction curves.  If such an equilibrium existed, at least one firm would not be on its reaction curve and  would therefore not be playing its optimal strategy. It has incentive to move elsewhere,  thus invalidating the equilibrium.  The Cournot equilibrium is a best response made in reaction to a best response and, by  definition, is therefore a Nash equilibrium. Unfortunately, the Cournot model does not  describe the dynamics behind reaching equilibrium from a non-equilibrium state. If the  two firms began out of equilibrium, at least one would have an incentive to move, thus  violating our assumption that the quantities chosen are fixed. Rest assured that for the  examples we have seen, the firms would tend towards equilibrium. However, we would  require more advanced mathematics to adequately model this movement. 
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This note was uploaded on 12/13/2011 for the course ECO 1320 taught by Professor Staff during the Fall '11 term at Texas State.

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An equilibrium cannot occur at a point not in the intersection of the two reaction curve1

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