Question

Two companies, X-Cola and Y-Cola are competing in selling carbonated beverages. Assume that the total market for their combined beverages is 1,000 bottles per day, and that each bottle sells for $1 (regardless of the brand or anything else). The companies can choose to advertise or not to advertise their products. Advertising costs $200 per day. If neither X-Cola nor Y-Cola choose to advertise or if both choose to advertise, they split the market equally, so each company sells 500 bottles per day. However, if only one company chooses to advertise while the other does not advertise, the company that does the advertising takes 80% of the market (800 bottles) while the other company is limited to just 20% of the market (200 bottles). These outcomes are summarized in the matrix below.

		X-COLA
	TOTAL SALES	NOT ADVERTISE	ADVERTISE
Y-COLA	NOT ADVERTISE	500/500	200/800
	ADVERTISE	800/200	500/500

a. Given this setup, construct another 2 by 2 matrix with profits by each firm in each scenario (that is, replace sales by profits in the matrix above).

(b) Based on this profits matrix, would you expect X-Cola to advertise or not? Would you expect Y-Cola to advertise or not? How is your answer related to the framework of the “Prisoner’s Dilemma” game?

(c) Suppose now that advertising costs $400 rather than $200 per day (and cannot be made cheaper). Would this change your answer to part (b)? Briefly explain your answer (no credit will be given without explanation)? [Hint: you may want to construct yet another 2 by 2 matrix with profits by each firm in each scenario with this new cost of advertising.]

Answer 1

(a) The pay-off matrices in terms of sales (as given) and profit (calculated) are shown below. The only differences are in the cells when they choose to advertise. For example, when both advertise, both of their sales = 500 and profit = 500 -200 = 300 (where 200 is the cost of advertising). When one of them advertises, then the profit for advertising advertising firm is derived from sales by deducting advertising cost, else profit = sales.

(b) If Y-Cola does not advertise, X-Cola will choose to advertise, because it gets higher profit (600) by advertising while it would get a profit of 200 if it chooses not to advertise. If X-Cola chooses to advertise, Y-Cola will change its strategy and it also decides to advertise, otherwise it would get a lower profit (200) as compared to (300). If Y-Cola chooses, to advertise, then X-Cola would not change its strategy and it would contiue with the strategy 'Advertise'. So, irrespective of the strategy of the other player, each one will choose to advertise. Hence, (advertise, advertise) = (300, 300) is the Nash equilibrium. This solution is similar to Prisoner's dillema, because they are not choosing the highest paying pay-offs because of non-cooperation,

(c) If advertising costs $400 instead of $200, the pay-off matrix becomes:

If Y-Cola does not advertise, X-Cola will choose to not to advertise, because it gets higher profit (500) by not advertising while it would get a profit of only 400 if it chooses to advertise. If X-Cola chooses not to advertise, Y-Cola will not change its strategy continue with the strategy not to advertise, otherwise it would get a lower profit (400) as compared to (500). We may observe that none of them have any incentive to change their strategy.

If Y-Cola advertises, X-Cola will choose not to advertise, because it gets higher profit (200) by not advertising while it would get a profit of only 100 if it chooses to advertise. If X-Cola chooses not to advertise, Y-Cola will change its strategy and it also decides not to advertise, otherwise it would get a lower profit (400) as compared to (500). So, irrespective of the strategy of the other player, each one will choose to not advertise. Hence, (not advertise, not advertise) = (500, 500) is the Nash equilibrium.

Now, the solution is different then (b)