Nash Equilibrium
The non-cooperative outcome shown in Figure 11-3 is called a Nash
equilibrium , after the U.S. mathematician John Nash, who developed
the concept in the 1950s and received the Nobel Prize in economics in
1994 for this work. (The 2002 movie A Beautiful Mind is about John Nash’s
life and contains a few fascinating bits of game theory!) In a Nash
equilibrium, each player’s best strategy is to maintain its current
behaviour given the current behaviour of the other players.
It is easy to see that there is only one Nash equilibrium in Figure 11-3
In the bottom-right cell, the best decision for each firm, given that the
other firm is producing two-thirds of the monopoly output, is to produce
two-thirds of the monopoly output itself. Between them, they produce a
factories, launch advertising campaigns, and adjust the prices
of their differentiated products.
Simple game theory and the prisoners’ dilemma also figure
prominently in the study of political science. Robert Axelrod’s
1984 book The Evolution of Cooperation discusses how the key
insights from the prisoners’ dilemma have been used in the
analysis of elections (where candidates’ choices are their
electoral platforms) and the nuclear arms race (in which
national governments’ choices are their decisions to build and
stockpile weapons).*