Electro World and Galaxy Appliance are competing retail stores that tacitly barg

Question

Electro World 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-price r gains $70 million and the high-price r gains $30 million. If both price low, each gains $40 million. Model this situation as a 2times2 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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