An East Coast West Coast Thing

Have you ever wondered why Jay Leno and David Letterman tape on different coasts? Elementary game theory can shed light upon the locating decisions of these leading late night hosts. Let us assume that ratings for each show are directly related to the average star power of the show’s guests. Thus, each host locates where his show can maximize guest star power given the locating decision of the other host. This objective narrows each show’s set of possible locations to two cities- Los Angeles and New York City. However, why don’t the hosts share one of the two cities? If both Leno and Letterman choose Los Angeles, they will compete fiercely for the strong but limited talent supply there, while largely neglecting the non-negligible talent supply available in New York City. A similar outcome will obtain if both locate in New York City. However, if Leno locates in one city and Letterman in another, each will hold monopsony power over his city’s celebrities. If a New York City based celebrity wishes to promote a new Broadway show, it will be costlier, in terms of time, for him to jet off to Los Angeles. Similarly, if a Los Angeles based celebrity wishes to promote her new movie, she is more apt to do so in Los Angeles.

A decision matrix can show us each show’s payoffs, in terms of average show rating, for each combination of show locations. In so doing, the matrix helps us understand what each party may choose to do, depending upon his beliefs about the other party. The first number in each cell of the matrix always refers to Leno’s payoff for a given outcome, and the second number always represents Letterman’s payoff.

There are a few notable characteristics of the payoff structure considered in the side table. Firstly, it is assumed that Los Angeles has the lion’s share of talent. If the two hosts locate in different cities, the one in Los Angeles will always come away with better ratings. Secondly, it is assumed that the two hosts are equally popular in a given location. In other words, their payoffs are strictly determined by their own location and the location of their partner. A Nash equilibrium outcome is an outcome whereby each person’s decision constitutes a best response to the other person’s action. This game features two Nash equilibria- one in which Leno is in Los Angeles and Letterman is in New York City and another in which Leno is in New York City and Letterman is in Los Angeles. That is to say, given a belief that his competitor will locate in one city, each host is best off to locate in the other. As we have set up the game, neither party wishes to split a single talent market.

If there are two possible Nash equilibria in this locating game, how did Leno end up in Los Angeles and Letterman in New York City? It may be random chance, within the game considered, that Leno got Los Angeles. It may be that Leno places a higher premium on warm weather than does Letterman, a fact that would alter each host’s payoffs. On the other hand, the nature of the locating game between these hosts might be more complex than that which we considered above. Recognizing that the Tonight Show was established in Los Angeles long before Letterman’s Late Show existed, we could consider the locating game as a sequential move game in which Leno enjoyed a first-mover advantage in Los Angeles and Letterman was thus dissuaded from entering that market. Also, we might consider assymetries in the popularity of the two hosts. Perhaps Leno receives what is perceived to be the bigger market because he is the more popular personality. Whatever complexities we add to the game, our original framework above suggests that no town is big enough for the both of Leno and Letterman.