Proctor & Gamble (p&g) Case Study

Firms in an oligopoly make many different decisions about how to compete: what prices to charge, how to advertise, location of facilities, product characteristics, and on. In practice, the inter‐dependence of firms’ payoffs with respect to these choices often has the structure of the “prisoners’ dilemma” game introduced in the last class. When firms interact repeatedly, it opens up rich possibilities for pricing strategies that maintain prices far above marginal cost.

Consider the pricing problem in the figure below. The payoffs in this matrix are from the Proctor & Gamble (P&G) and Unilever pricing example. As shown in the payoff table, when both firms price at $1.40, each firm’s profit is $72K per month. Figure includes a higher pricing point of $1.50, and the actual profit (in ‘000 $ per month) the two firms expected at those pricing points.

 [pic 1]

If this game was played only once, then you can quickly verify the only stable prices in this market are the Nash solution: Both firms price at [$__①___].

1. 풀이

P&G가 1.4를 선택할 경우, Unilever는 1.4를 선택해야 72K를 동일하게 얻을 수 있으며,

P&G가 1.5를 선택할 경우에도, Unilever는 1.5를 선택해 80K를 얻기 보다 1.4를 선택해 89K를 얻는 것이 이익이므로 1.4를 선택하게 됨

Unilever가 먼저 선택하고, P&G가 나중에 가격을 결정하더라도 동일한 결과임.

따라서 양사의 가격은 [$___1.4____]

Now suppose that the two firms will interact repeatedly—and that each can update its price monthly. Can a “cooperative” strategy in which both firms price at $1.50 be sustained?  Depending on demand, cost, and interest rate conditions, the answer is often yes.

Consider the following strategy for, say, P&G, called a Grim Trigger Strategy (GTS):

Grim Trigger Strategy: Begin by cooperating.  As long as the game continues and as long as both players have cooperated by pricing at $1.50, continue to cooperate by pricing at $1.50.  If any player cuts price, then continue to price at $1.40 ever after.

If Unilever cooperates: What is Unilever’s best response to this strategy?  Suppose first that Unilever responds by always pricing at $1.50. Since this game is dynamic, we need to consider the time value of money to Unilever’s management.  Let’s suppose they discounts future profits at a rate of ra = 25% per annum, which corresponds to a monthly rate of approximately rm = 1.877%. (Parenthetically: This relation is ra = (1 + rm)12 − 1.)