sign, as in the payoff −3, is that ATV will lose an audience of 3 million. The +
payoffs are good for ATV and the − payoffs are good for BTV.
We’ll assume the companies make their one-off decisions on the basis of the
payoff table and that they make their bids simultaneously by sealed bids.
Obviously both companies act in their own best interests.
If ATV chooses Scotland the worst that could happen would be a loss of 3
million; if it bids for England, the worst would be a gain of 2 million. The
obvious strategy for ATV would be to choose England (row 2). It couldn’t do
worse than gain 2 million viewers whatever BTV chooses. Looking at it
numerically, ATV works out −3 and 2 (the row minimums) and chooses the row
corresponding to the maximum of these.
BTV is in a weaker position but it can still work out a strategy that limits its
potential losses and hope for a better payoff table next year. If BTV chooses
Scotland (column 1) the worst that could happen would be a loss of 5 million; if
it chooses England, the worst would be loss of 4 million. The safest strategy for
BTV would be to choose England (column 2) for it would rather lose an audience
of 4 million than 5 million. It couldn’t do worse than lose 4 million viewers
whatever ATV decides.
A beautiful mind
John F. Nash (b.1928) whose troubled life was portrayed in the 2001 movie A Beautiful
Mind won the Nobel Prize for Economics in 1994 for his contributions to game theory.
Nash and others extended game theory to the case of more than two players and to
games where cooperation between players occurs, including ganging up on a third
player. The ‘Nash equilibrium’ (like a saddle point equilibrium) gave a much broader
perspective than that set down by von Neumann, resulting in a greater understanding
of economic situations.
These would be the safest strategies for each player and, if followed, ATV
would gain 4 million extra viewers while BTV loses them.
When is a game determined?
The following year, the two TV companies have an added option – to operate
in Wales. Because circumstances have changed there is a new payoff table.