The widget market is controlled by two firms: Acme Widget Company and Widgetway Manufacturing. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells widgets at the price for the duration of the period. There is very little brand loyalty among widget buyers so that each firm's demand is highly elastic. Each firm's prices are thus very sensitive to inter-firm price differentials. The two firms must choose between a high and low price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway's profit is before the comma, Acme's is after the comma.
a. Does either firm have a dominant strategy? What strategy should each firm follow?
b. Assume that the game is to be played an infinite number of times. (Or, equivalently, imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy would be a reasonable choice? Explain this strategy.
c. Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational?

Question

The widget market is controlled by two firms: Acme Widget Company and Widgetway Manufacturing. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells widgets at the price for the duration of the period. There is very little brand loyalty among widget buyers so that each firm's demand is highly elastic. Each firm's prices are thus very sensitive to inter-firm price differentials. The two firms must choose between a high and low price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway's profit is before the comma, Acme's is after the comma.  
a. Does either firm have a dominant strategy? What strategy should each firm follow?
b. Assume that the game is to be played an infinite number of times. (Or, equivalently, imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy would be a reasonable choice? Explain this strategy.
c. Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational?

Quizplus · Accepted Answer

The Answer of The widget market is controlled by two firms: Acme Widget Company and Widgetway Manufacturing. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells widgets at the price for the duration of the period. There is very little brand loyalty among widget buyers so that each firm's demand is highly elastic. Each firm's prices are thus very sensitive to inter-firm price differentials. The two firms must choose between a high and low price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway's profit is before the comma, Acme's is after the comma.  
a. Does either firm have a dominant strategy? What strategy should each firm follow?
b. Assume that the game is to be played an infinite number of times. (Or, equivalently, imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy would be a reasonable choice? Explain this strategy.
c. Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational?

The Widget Market Is Controlled by Two Firms: Acme Widget