Consider two single-malt whiskey distillers, Laphroaig and Knockando. If they advertise, they can both sell more whiskey and increase their revenue. However, the cost of advertising more than offsets the increased revenue so that each distiller ends up with a lower profit than if they do not advertise. On the other hand, if only one advertises, that distiller increases its market share and also its profit.
a. Construct a payoff matrix using the following hypothetical information: If neither distiller advertises, each earns a profit of $35 million per year. If both advertise, each earns a profit of $20 million per year. If one advertises and the other does not, the distiller who advertises earns a profit of $50 million and the distiller who does not advertise earns a profit of $9 million.
b. If Laphroaig wants to maximize profit, will it advertise? Briefly explain.
c. If Knockando wants to maximize profit, will it advertise? Briefly explain.
d. Is there a dominant strategy for each distiller? Briefly explain.

a)                                 Advertising               Not advertising

Advertising   $20 million, $20 million  $50 million, $9  million

Not Advertising  $9 million, $50 million       $35 million, $35 million

b)  If Laphroaig wants to maximize profit, it will advertise only when Knockando does not advertise.

c)  If Knockando wants to maximize profit, it will advertise only when Laphroaig does not advertise.

e) No, there is no dominant strategy for each distiller.

Explanation:

a)  A payoff matrix is a visual representation of all the possible strategies and all of the possible outcomes. Below is the payoff matrix for the distillers:

                         Advertising               Not advertising

Advertising   $20 million, $20 million  $50 million, $9  million

Not Advertising  $9 million, $50 million       $35 million, $35 million

b) If Knockando does not advertise then Laphroaig gets $50 millions of profit if Laphroaig advertises. If Knockando does not advertise and Laphroaig does not advertise then Laphroaig will get only $35 million. If both do advertise, they both get $20 million.  If Knockando does advertise and Laphroaig does not advertise then Laphroaig earns a profit of $9 million.  If Laphroaig wants to maximize profit, it will advertise only when Knockando does not advertise.

c)  Same conditions as in b) Therefore, If Knockando wants to maximize profit, it will advertise only when Laphroaig does not advertise.  

d) No, there is no dominant strategy for each distiller. If the two distillers agree to coordinate their strategy means both of them can decide not to advertise to earn a profit of $35 million per year each which is better than when both advertise.

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