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Best Buy (B) and Circuit City (C) are competitors in the consumer electronics market. Both have relatively large margins on plasma TV's. Essentially, they have driven up the price of such TV's well above marginal costs because consumers of these TVs tend to be wealthy, and thus tend to have less time, and thus tend to be less price sensitive. However, some consumers will shop around and thus each Firm could steal business from the other by cutting prices.

Circuit City
Hold and match prices Cut prices
Best Buy Hold and match prices B=8, C=8 B=4, C=10
Cut prices B=10, C=4 B=6, C=6

a. Calculate all (if any) dominant strategies.

b. Calculate all (if any) Nash equilibria. For each calculate the profits for each firm.

c. Rank all of the payoffs from highest to lowest social benefit. Does the Nash equilibrium correspond to the highest social benefit? Why or why not?

d. Suppose both firms introduce a price matching policy. Calculate the new payoff matrix and repeat (a) and (b).

Solution Preview

See attached file.

1. Dominant strategies

For best buy, its dominant strategy (hereafter DS) is cut price. You can easily see that if CC cuts price, BB is better off cutting price (if CC cuts, BB gets 6 for cut and only 4 for not cut). If CC does not cut price, BB is still better off cutting price (if CC does not cut, BB gets 10 for cut, 8 for not cut). Hence cut price is a DS for best buy.

Similarly, cut ...