Analyzing Payoff Tables 403to NBC and CBS (two of the ratings leaders during the last decade) and focus
on their programming decisions for the 8-to-9 P.M. and 9-to-10 P.M. slots on a
particular weeknight. The networks must decide which hour-long programs
from last season to pencil into the slots. Each network’s main concern is when
to schedule its hit show—at 8 P.M. or 9 P.M. The other time slot will be filled by
a run-of-the-mill program.
Here the focus of competition is between two players, NBC and CBS.
Each network has two possible actions, or strategies: to run its hit show at
8 P.M. or at 9 P.M. The essential elements of any two-player competitive decision
can be described by a two-dimensional payoff table. According to the stan-
dard format, the first player’s alternative actions are listed along the rows of
the table; the second player’s possible actions are listed along the columns.
The payoff table in Table 10.1 is an example. NBC’s possible actions are listed
along the rows and CBS’s actions along the columns. For any combination of
actions, the resulting payoffs to the networks are shown under the corre-
sponding row and column. By convention, the first (i.e., row) player’s payoff
is listed first. In the table, each network’s payoff is measured by the projected
totalnumber of viewers (in millions) over the two-hour period. For instance,
if each network leads with its hit show at 8 P.M., NBC’s audience will be 36 mil-
lion viewers and CBS’s will be 33 million. The table also shows the number
of viewers during each hour. Although the disaggregated figures are of
some interest in their own right, what ultimately matters to each network is
its total audience.^2(^2) The hourly viewer numbers reflect a number of facts. First, the total number of viewers is larger
during the 8-to-9 P.M. slot than during the 9-to-10 P.M. slot. Second, during a given hour, the more
highly rated a network’s show (and the less highly rated its competitor), the larger the network’s
audience. Third, a portion of viewers watching a network’s show from 8 to 9 P.M. continues to stay
tuned to that network during the 9-to-10 P.M. slot.
TABLE 10.1
A TV Ratings Battle
Each network’s domi-
nant strategy is to
schedule its hit at
8 P.M. The left-hand
entry in each cell lists
NBC’s total number
of viewers (in millions).
The right-hand entry
lists CBS’s total viewers.
Figures in parentheses
divide total viewers
between 8 P.M. and 9 P.M.
CBS
Schedule Hit Schedule Hit
at 8 P.M. at 9 P.M.
Schedule Hit 36 33 39 28
at 8 P.M. (2115) (1914) (2514) (1117)
NBC
Schedule Hit 30 36 32 30
at 9 P.M. (1317) (2016) (1616) (16 (^14) )
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