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Topic: Chapter 7 payoffs in Figure 7.7-7.9
Conf: Corrections and Errata, Msg: 6722
From: Reiko Aoki (r.aoki@auckland.ac.nz)
Date: 5/6/2001 07:19 AM

Chapter 7 payoffs in Figure 7.7-7.9 Reiko Aoki sarahberry r.aoki@auckland.ac.nz Please correct me if I am wrong:
I) I have had trouble with payoffs in Figure 7.7
1) In the Figure 7.7 right matrix (when firm2 is high cost), should 1's payoff when p1=4,p2H=4 be 16, assuming 1 gets all the demand 8-4, not (4-0)*(8-4)/2=8 ? Seems in the left matrix (when firm2 is low cost), 1's payoff when p1=1, p2L=1 assumes that 1 gets total demand 8-1 and gets (1-0)*(8-1)=7. The rules for allocating demand when firms have same prices equal to higher MC are not consistent. If I am correct, this will also change firm 1's payoff in Figure 7.8 first matrix (p1=4) when p2L=4, p2H=4 to 12 ?

2) Figure 7.7, right matrix, firm2's payoff when p1=p2H=6 should be 2, not -2. Profit is (6-4)*(8-6)/2. Accordingly, in Figure 7.8, first matrix (when p1=6), firm2's payoff when p2h=6 should be 2. This seems to make p2h=4 no longer dominant strategy (as claimed in the text based on payoff -2).

II) Regarding Figure 7.9,
1) There is no mention of taking 4 coins away so r4 should not be there.
2) THere is obviously typos in some of the payoffs - player 2 does not always win.