Suppose that Creamland and Dairy King are the only two firms that sell ice cream

Question

Suppose that Creamland and Dairy King are the only two firms that sell ice cream. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: For example, the upper right cell shows that if Creamland advertises and Dairy King doesn't advertise, Creamland will make a profit of $18 million, and Dairy King will make a profit of $2 million. Assume this is a simultaneous game and that Creamland and Dairy King are both profit-maximizing firms. If Creamland decides to advertise, it will earn a profit of million if Dairy King advertises and a profit of million if Dairy King does not advertise. If Creamland decides not to advertise, it will earn a profit of million if Dairy King advertises and a profit of million if Dairy King does not advertise. If Dairy King advertises, Creamland makes a higher profit if it chooses If Dairy King doesn't advertise, Creamland makes a higher profit if it chooses Suppose that both firms start off not advertising. If the firms act independently, what strategies will they end up choosing? Again, suppose that both firms start off not advertising. If the firms decide to collude, what strategies will they end up choosing?

Explanation / Answer

A game is the strategic interaction between two or more players in the process of economic decision making. Each agent who makes the decision in a game is called the player. Each player has a set of choices to decide upon, these choices are called the strategies. The strategies are tied to certain outcomes called payoffs.

In the game above, if C decides to advertise, it will earn a profit of $10 million if D advertises and a profit of $18 million if D does not advertise.

Again, if C decides not to advertise, it will earn a profit of $2 million if D advertises and a profit of $11 million if D does not advertise.

If D advertises, C makes a higher profit if it choses advertise.

If D doesn't advertises, C makes a higher profit if it choses advertise.

The move that the player choses no matter what the other player do is called the dominant strategy. The move that a player never plays no matter what the other player do is called the dominated strategy. The equilibrium where each player plays their dominant strategies is called the dominant strategy equilibrium.

In this case C has a dominant strategy "advertise" because it will gave the firm higher payoff no matter what strategy the other player choses.

Similarly, if D decides to advertise, it will earn a profit of $10 million if C advertises and a profit of $18 million if C does not advertise.

Again, if D decides not to advertise, it will earn a profit of $2 million if C advertises and a profit of $11 million if C does not advertise.

If C advertises, D makes a higher profit if it choses advertise. If C doesn't advertises, D makes a higher profit if it choses advertise.

n this case D has a dominant strategy "advertise" because it will gave the firm higher payoff no matter what strategy the other player choses.

Therefore, C will always decide to advertise and D will always decide to advertise as well.

Suppose both the firm start off not advertising, If firm act independently,

If both firm collude. They will act as a single firm and the pay off matrix will be

DK

C

Advertise

Doesn’t Advertise

Advertise

10+10=20

18+2=20

Doesn’t Advertise

2+18=20

11+11=22

Suppose both the firm start off not advertising, If both firm collude,

DK

C

Advertise

Doesn’t Advertise

Advertise

10+10=20

18+2=20

Doesn’t Advertise

2+18=20

11+11=22

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