Chapter-2 - Chapter 2:Building a Game Reality is very...

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Chapter 2:Building a Game A literal model : accurate description of the real- world setting. A metaphorical model : a vast simplification – a simplified analogy – for the real world situation. • Game Theory uses metaphorical models. A literal model : accurate description of the real- world setting. A metaphorical model : a vast simplification – a simplified analogy – for the real world situation. • Game Theory uses metaphorical models. Reality is very complex What to put in a model (what to pack for college)
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Extensive Form Games A description of the sequence of choices faced by those involved in the strategic situation. • A set of players • When a player moves • What can a player choose when it’s his turn to move • What the player knows when it’s his turn to move A description of the sequence of choices faced by those involved in the strategic situation. • A set of players • When a player moves • What can a player choose when it’s his turn to move • What the player knows when it’s his turn to move
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• Two players: the kidnapper (Guy); the victim’s wife (Vivica). • Sequence of events: • Guy decides whether to kidnap (game over if no kidnap) • Vivica is contacted for ransom • After observing Vivica’s decision, Guy decides whether to kill or release the victim. • Two players: the kidnapper (Guy); the victim’s wife (Vivica). • Sequence of events: • Guy decides whether to kidnap (game over if no kidnap) • Vivica is contacted for ransom • After observing Vivica’s decision, Guy decides whether to kill or release the victim. A Kidnapping Game
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1 4 2 2 5 3 4 1 3 5 Release Release Kill Kill Guy Guy Guy Vivica Do not pay ransom Pay ransom Guy Vivica Do not kidnap Kidnap Decision Tree
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Explanations for Decision Tree • Read from top to bottom (left to right). • Each of the dots is called a decision node Represents a point in the game at which someone has a decision to make. • Come out of a decision node is a series of branches Each branch represents a different action available to the decision maker. • The ending nodes are called terminal nodes Represents “game over”. • Read from top to bottom (left to right). • Each of the dots is called a decision node Represents a point in the game at which someone has a decision to make. • Come out of a decision node is a series of branches Each branch represents a different action available to the decision maker. • The ending nodes are called terminal nodes Represents “game over”.
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Rank the Outcomes Five possible outcomes No kidnapping (a) Kidnapping, ransom, killed (b) Kidnapping, ransom, released (c) Kidnapping, no ransom, killed (d) Kidnapping, no ransom, released (e) Five possible outcomes No kidnapping (a) Kidnapping, ransom, killed (b) Kidnapping, ransom, released (c) Kidnapping, no ransom, killed (d) Kidnapping, no ransom, released (e) Guy’s ranking: (c) > (b) > (a) > (e) > (d) • Vivica’s ranking: (a) > (e) > (c) > (d) > (b) Guy’s ranking: (c) > (b) > (a) > (e) > (d) • Vivica’s ranking: (a) > (e) > (c) > (d) > (b)
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Assigning Payoffs
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This note was uploaded on 07/17/2008 for the course ECON 601 taught by Professor Yang during the Spring '08 term at Ohio State.

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Chapter-2 - Chapter 2:Building a Game Reality is very...

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