Decision Making using Game Theory: An introduction for managers

120Two-person mixed-motive games of strategyA c 1Reaction function forSmurfit-StoneA c 2(A c 2 ) /2(A + c 1 2c 2 ) / 3CNR 2R 1Nash equilibrium (also the Cournotequilibrium)TReaction function forInternational Paper(A 2c 1 + c 2) / 3(A c 1) /2Figure 6.11The Cournot–Nash equilibrium.the two iso-proWt curves are mutually perpendicular.Although the concept of the Nash equilibrium has provided asolution, Cournot arrived at the same solution in a diVerent way. Heanalysed how the two Wrms would behave if they were out of equilibrium.Figure 6.12 shows the reaction functions for SmurWt-Stone andInternational Paper. Say initially that SmurWt-Stone is operating amonopoly, it will produce (A c 1 )/2 tonnes of linerboard. If InternationalPaper now enters the market and assumes that SmurWt-Stonewill maintain that production level, it will produce at a level verticallyabove that point, but on its own reaction curve. This point is oV theSmurWt-Stone reaction curve, so SmurWt-Stone will move its productionlevel horizontally onto its own reaction curve. This incrementalprocess continues, in a zigzag fashion, until the Cournot equilibriumpoint (C) is reached, at the intersection of the two reaction curves.The Nash and Cournot approaches produce the same solution, butthe Cournot concept is weaker because it supposes that one Wrm is ableto react to the other Wrm’s entry to the market, contradicting thegame’s assumption of ‘static-ness’ or simultaneity. The concept of