At a time when demand for ready-to-eat cereal was stagnant, a spokesperson for t

Question

At a time when demand for ready-to-eat cereal was stagnant, a spokesperson for the
cereal maker Kellogg’s was quoted as saying “…for the past several years, our
individual company growth has come out of the other fellow’s hide.” Kellogg’s has
been producing cereal since 1906 and continues to implement strategies that make it
a leader in the cereal industry. Suppose that when Kellogg’s and its largest rival
advertise, each company earns $0 billion in profits. When neither company
advertises, each company earns profits of $8 billion. If one company advertises and
the other does not, the company that advertises earns $48 billion and the company
that does not advertise loses $1 billion. Under what conditions could these firms use
trigger strategies to support the collusive level of advertising?

Explanation / Answer

In game theory, a trigger strategy is any of a class of strategies employed in a repeated non-cooperative game. A player using a trigger strategy initially cooperates but punishes the opponent if a certain level of defection (i.e., the trigger) is observed. The level of punishment and the sensitivity of the trigger vary with different trigger strategies. Notice that, in the above game, one successful cheat is worth $48 billion, one successful cooperation is only worth $8 billion, and both firms earn nothing if they both advertise. 48/8 = 6 So, in order for one firm to induce the other firm to cooperate, it has to threaten to advertise for six consecutive rounds or more. The opportunity cost will now be greater than or equal to the profit earned for the firm thinking about cheating. In order for this to be a credible threat, the firm will have to be able to endure the $1 billion loss that it would incur from the cheat for the following four rounds while earning no new profit. That is, the initial loss can't be enough to put the firm out of business for future rounds or cause it to not have enough money to advertise. If both firms make credible threats to advertise for six or more consecutive rounds, then the long-term Nash equilibrium for the repeated game is that neither firm will advertise.

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