Ch28 - Chapter Twenty-Eight Game Theory Game Theory x Game...

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Chapter Twenty-Eight Game Theory
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Game Theory Game theory models 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.
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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.
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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 strategies.
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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 strategy 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 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. Player B Player A L R U D (3,9) (0,0) ( 1 , 8 ) (2,1)
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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. Player B Player A L R U D (3,9) (0,0) (1,8) ( 2 , 1 )
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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)
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An Example of a Two-Player Game What plays are we likely to see for this game? Player B Player A L R U D (3,9) (0,0) (1,8) (2,1)
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An Example of a Two-Player Game Player B Player A Is (U,R) a likely play? L R U D (3,9) (0,0) ( 1 , 8 ) (2,1)
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An Example of a Two-Player Game Player B Player A 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. Is (U,R) a likely play? L R U D (3,9) (0,0) ( 1 , 8 ) (2,1)
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An Example of a Two-Player Game Player B Player A Is (D,R) a likely play? L R U D (3,9) (0,0) (1,8) ( 2 , 1 )
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An Example of a Two-Player Game Player B Player A Is (D,R) a likely play? If B plays Right then A’s best reply is Down. L R U D (3,9) (0,0) (1,8) ( 2 , 1 )
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An Example of a Two-Player Game Player B Player A If B plays Right then A’s best reply is Down. If A plays Down then B’s best reply is Right. So (D,R) is a likely play. Is (D,R) a likely play? L R U D (3,9) (0,0) (1,8) ( 2 , 1 )
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An Example of a Two-Player Game Player B Player A Is (D,L) a likely play?
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