I agree that F(n) is likely to decline after reaching a peak.
I would also suggest, however, that there is another variable at play. The total reward a player receives from the game includes intermediate rewards (from laughter) after each turn... which could be referred to as the humourous_connection variable. These will also have some dependency upon the state of the ISIHAC audience but, critically, also upon the relationship between the station being announced and the one previous to it.
If this intermediate reward was equal at every step (a simplification), then it could largely be discounted. However, by definition, the first move does not attract this reward so player one might also be motivated by an urge to 'catch up' making him more likely to call Mornington Crescent.
Also, either player might be more motivated to end the game on their move after the opponent has won a particularly large intermediate award. This means both players will need to juggle their perceptions of total reward gained so far against the value of the terminal reward and, possibly, if they think they have an alternative station with a high humourous_connection score, whether to play that instead.