Varian_Chapter28_Game_Theory

# Varian_Chapter28_Game_Theory - Chapter28 GameTheory...

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Chapter 28 Game Theory

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Game Theory Game theory helps to model 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;  e.g.  OPEC The study of externalities;  e.g.  using a  common resource such as a fishery. The study of military strategies. Bargaining. How markets work.

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What is a Game? game  consists of a set of  players a set of  strategies  for each player the  payoffs  to each player for every  possible choice of strategies 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 actions.

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An Example of a Two-Player  Game The players are called A and B. Player A has two actions, called “Up” and  “Down”. Player B has two actions, called “Left” and  “Right”. The table showing the payoffs to both players  for each of the four possible action  combinations 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)

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An Example of a Two-Player  Game A play of the game is a pair such as (U,R) where  the 1st element is the action chosen by Player A  and the 2nd is the action chosen by Player B. L R U D (3,9) (0,0) (1,8) (2,1) Player B Player A
An Example of a Two-Player  Game E.g.  if A plays  U p and B plays  R ight then A’s payoff  is  1  and B’s payoff is  8 . This is the game’s payoff matrix. L R U D (3,9) (0,0) ( 1 , 8 ) (2,1) Player B Player A

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An Example of a Two-Player  Game And if A plays  D own and B plays  R ight then A’s  payoff is  2  and B’s payoff is  1 . This is the game’s payoff matrix. L R U D (3,9) (0,0) (1,8) ( 2 , 1 ) Player B Player A
An Example of a Two-Player  Game What plays are we likely to see for this game? L R U D (3,9) (0,0) (1,8) (2,1) Player B Player A

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An Example of a Two-Player  Game If B plays Right then A’s best reply is Down since  this improves A’s payoff from 1 to 2.  So (U,R) is  not a likely play.
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## This note was uploaded on 03/03/2011 for the course ECON 206 taught by Professor Ioanadan during the Spring '10 term at University of Toronto.

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Varian_Chapter28_Game_Theory - Chapter28 GameTheory...

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