Two radio stations compete for advertisers.  They run ads during 10 minute slots that they can locate anywhere within a given hour of air time.  They know that listeners don’t like ads and will switch to another station to avoid them.  Will their commercial times be disjoint, overlapping or will they exactly coincide?

Whatever they do, the listeners will adjust their behavior.  Disjoint advertising intervals would mean that listeners, regardless of which station they are currently tuned to, will switch as soon as the ads start and always be listening to music.  So that’s not an equilibrium.

Suppose they overlap.  Radio station B is trying to be clever by starting its ads just a minute later than A.  Those listening to radio station A switch to B when the ads start to get an extra minute of music.  But when the ads start on B, the listeners know that the music will begin sooner on radio station A.  But since you don’t know exactly when the ads will end, and in the meantime you have ads on either station, the time to switch to A is now.  That’s not an equilibrium either.

If the ad intervals exactly coincide then listeners learn there is no point in switching.  And if listeners aren’t switching then the stations can do no better than to have their ad intervals coincide.  So that’s the equilibrium.

This paper by Andrew Sweeting shows empirically that stations coordinate their advertising intervals and explores the motives.

My simple model omits NPR.  What programming runs on public radio during the ad intervals on commercial radio?  Do commercial radio stations change their behavior during NPR pledge drives?