A. How does this matrix demonstrate mutual interdependence between the firms? B.

Question

 

A.   How does this matrix demonstrate mutual interdependence between the firms?


B.  Define the term dominant strategy. Assume the firms play a non-repeated game without collusion. Does Acme have a dominant strategy? If so, what is it? What about Ajax?


C.  Define the term Nash equilibrium. Assume the firms play a non-repeated game without collusion. What is the Nash equilibrium for this game?

Consider the game theory matrix below in which the numerical data show the profits resulting from alternative combinations of advertising strategies for Ajax and Acme. Ajax's profits are shown in the upper right part of each cell; Acme's profits are shown in the lower left. Both firms have full knowledge of the matrix. Answer each of the following questions, in one or two sentences A. How does this matrix demonstrate mutual interdependence between the firms? B. Define the term dominant strategy. Assume the firms play a non-repeated game without collusion. Does Acme have a dominant strategy? If so, what is it? What about Ajax? C. Define the term Nash equilibrium. Assume the firms play a non-repeated game without collusion. What is the Nash equilibrium for this game?

Explanation / Answer

Let us first look at the strategies by comparing payoffs. Acme compares the first column vertically and Ajax compares columns horizontally.

800   800     1200  600

600 1200     1000 1000


A. We can see the mutual independence based on the dominant strategies of the firms. In this case, Acme and Ajax both want to choose large budget indpendently of each other.

B. Dominiant strategy is to choose large budget. Acme will choose large budget. Ajaz will choose large budget.

C. Nash equilibrium is when players always choose the best strategy no matter the other players decision. In this case, Nash Equilibrium is box A (large budget, large budget).

Hope this helps

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