文档介绍：Chapter Twenty-Eight
Game Theory
Game Theory
Game theory models strategic behavior by agents who understand that their actions affect the actions of other agents.
Some Applications of Game Theory
The study of oligopolies (industries containing only a few firms)
The study of cartels; . OPEC
The study of externalities; . using mon resource such as a fishery.
The study of military strategies.
What is a Game?
A game consists of
a set of players
a set of strategies for each player
the payoffs to each player for every possible list of strategy choices by the players.
Two-Player Games
A game with just two players is a two-player game.
We will study only games in which there are two players, each of whom can choose between only two strategies.
An Example of a Two-Player Game
The players are called A and B.
Player A has two strategies, called “Up” and “Down”.
Player B has two strategies, called “Left” and “Right”.
The table showing the payoffs to both players for each of the four possible binations is the game’s payoff matrix.
An Example of a Two-Player Game
This is the game’s
payoff matrix.
Player B
Player A
Player A’s payoff is shown first. Player B’s payoff is shown second.
L
R
U
D
(3,9)
(0,0)
(1,8)
(2,1)
An Example of a Two-Player Game
. if A plays Up and B plays Right then A’s payoff is 1 and B’s payoff is 8.
This is the game’s
payoff matrix.
Player B
Player A
L
R
U
D
(3,9)
(0,0)
(1,8)
(2,1)
An Example of a Two-Player Game
And if A plays Down and B plays Right then A’s payoff is 2 and B’s payoff is 1.
This is the game’s
payoff matrix.
Player B
Player A
L
R
U
D
(3,9)
(0,0)
(1,8)
(2,1)
An Example of a Two-Player Game
Player B
Player A
A play of the game is a pair such as (U,R)
where the 1st element is the strategy
chosen by Player A and the 2nd is the
strategy chosen by Player B.
L
R
U
D
(3,9)
(0,0)
(1,8)
(2,1)