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Extra info for Econometrica 2010 Vol.78 No.2
The leader’s prize falls as the follower moves further down its learning curve because it takes progressively longer for the leader to force the follower back up its learning curve and because the lower cost of the follower makes it harder for the leader to do so. In the unlikely event that the follower crashes through the sideways trench in state (26 8), the leader’s prize falls sharply. At the same time, the follower’s prize rises sharply as it turns from a docile competitor into a viable threat.
488 BESANKO, DORASZELSKI, KRYUKOV, AND SATTERTHWAITE TABLE III EXTRA-TRENCHY EQUILIBRIUM (ρ = 0 85, δ = 0 08) Leader Follower State Cost Prize Price Prob. Value Cost Prize Price Prob. 08 7) 8) 9) 10) Sideways Trenches A sideways trench, as seen in the lower right panel of Figure 4, is a price war between very asymmetric firms. This war is triggered when the follower starts to move down its learning curve. Table III provides details on firms’ competitive positions in various states for our leading example of an extratrenchy equilibrium (ρ = 0 85, δ = 0 08).
More generally, as Figure 3 shows, in the absence of organizational forgetting, asymmetries are modest if they arise at all. Although ID and IID hold, the maximum expected Herfindahl index across all equilibria is 0 67 (attained at ρ = 0 65). Hence, ID and IID are not sufficient for economically meaningful market dominance. ID and IID are also not necessary for market dominance. The extra-trenchy equilibrium (ρ = 0 85, δ = 0 08), for example, violates ID and thus IID. Yet, the industry is likely to be a near monopoly at all times.