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. 
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    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.
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    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 .
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    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
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    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
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    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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Varian_Chapter28_Game_Theory - Chapter28 GameTheory...

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