SEQUENTIAL GAMES
In some games, the order of moves matters. For example,
in a bicycle race with a staggered start, it may help to go
last and thus know the time to beat. On the other hand,
competition to establish a new high-definition video format
may be
Dominant Strategies
(Fink, fink) is a Nash equilibrium in the Prisoners Dilemma because finking is a best response
to the other players finking. We can say more: finking is the best response to all of the other
players strategies, fink and silent. (This c
EXISTENCE
One of the reasons Nash equilibrium is so widely used is that a Nash equilibrium is
guaranteed to exist in a wide class of games. This is not true for some other equilibrium
concepts. Consider the dominant strategy equilibrium concept. The Priso
MIXED STRATEGIES
Players strategies can be more complicated than simply choosing an action with certainty. In
this section we study mixed strategies, which have the player randomly select from several
possible actions. By contrast, the strategies consider
Nash equilibrium in the Prisoners Dilemma
Let s apply the concepts of best response and Nash equilibrium to the example of the
Prisoners Dilemma. Our educated guess was that both players will end up fi nking. We will
show that both fi nking is a Nash equi
Strategy and Game Theory
Players
Each decision maker in a game is called a player. These players may be individuals (as in poker
games), firms (as in markets with few firms), or entire nations (as in military conflicts). A player
is characterized as havin
NASH EQUILIBRIUM
In the economic theory of markets, the concept of equilibrium is developed to indicate a
situation in which both suppliers and demanders are content with the market outcome. Given
the equilibrium price and quantity, no market participant
Thinking strategically about the Prisoners Dilemma
Although we have not discussed how to solve games yet, it is worth thinking about what we
might predict will happen in the Prisoners Dilemma. Studying Table 8.1, on first thought
one might predict that bo
PRISONERS DILEMMA
The Prisoners Dilemma, introduced by A.W. Tucker in the 1940s, is one of the most
famous games studied in game theory and will serve here as a nice example to illustrate
all the notation just introduced. The title stems from the followin
Tragedy of the Commons
Example 8.6 illustrates how to solve for the Nash equilibrium
when the game (in this case, the Tragedy of the Commons)
involves a continuum of actions. The first step is to write down
the payoff for each player as a function of all