ElectroWorld and Galaxy Appliance are competing retail stores that tacitly barga

Question

ElectroWorld and Galaxy Appliance are competing retail stores that tacitly bargain with each
other in deciding pricing policies. Each can either price high or price low. If both price high, payoffs
to each are $50 million; if one prices high and the other low, the low-pricer gains $70 million
and the high-pricer gains $30 million. If both price low, each gains $40 million. Model this
situation as a 2 X 2 game, and identify the equilibrium. How would this change if each of the
retailers, as part of the bargaining, committed to a price-matching guarantee, where one would
match any low price from the other?

Explanation / Answer

This is a Prisoner's Dilemma with a twist. The original matrix without the price-matching has only one equlibrium (Low, Low), because Low dominates High (just as in any other PD.) With price matching, however, there is no way to get the $70 payoff by choosing Low when the other person chooses High. As strange as it sounds, this breaks the dominance of Low over High. Now choosing Low guarantees a profit of only $40, whereas choosing High gives a profit of $50 if the other guy chooses High too. Now (High, High) and (Low, Low) are BOTH Nash equilibria. Note that (Low, Low) is NOT eliminated as a Nash equilibrium; even with the price guarantee, if the other guy is choosing Low, you can't do better by choosing High. (Choosing High weakly dominates choosing Low, but only weakly.) There is an interesting opportunity for tacit collusion if the game is repeated; alternating (High, Low) and (Low, High) yields the same average profit as choosing (High, High) all the time, even without the orice guarantee.

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