class13_seqGame_

class13_seqGame_ - Econ 51 Winter 2011 Class#13 PS#4 is due...

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1 Econ 51, Winter 2011 Class #13 • PS #4 is due Friday. • PS #5 posted today, due Friday next week • Today: Start with sequential and repeated games. Wednesday, February 16, 2011
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2 Game theory: Sequential Games • We finished last time with showing how to solve for equilibrium in mixed strategies. • We will away from simultaneous decisions, and start talking about sequential (extensive-form) games. Wednesday, February 16, 2011
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3 Sequential (extensive-form) games Game theory So far we only considered games in which every player had to simultaneously (or secretly) decide which strategy to choose. In real life, however, many games are decided sequentially: first one player takes an action, then the other one. Most important, once the other takes her action, she already knows what the first player did. Therefore, we will now consider games in which players play in sequence (over time), with the action of each turn realized before other players take their actions. To capture the sequential structure of the game, we will use game trees to depict these games. Wednesday, February 16, 2011
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4 Example 1: entry game Game theory Recall the simultaneous entry game from last week: Fight Don’t Fight Enter -2,2 5,5 Stay out 0,8 0,10 Suppose now the incumbent firm can move first: they can take a massive (but costly) advertising campaign, which will commit itself to cut prices (i.e. fight the entrant). How can we model this? Entrant Incumbent Wednesday, February 16, 2011
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5 Entry game (cont.) Game theory A game tree: What will happen? Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Wednesday, February 16, 2011
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6 Entry game (cont.) Game theory A game tree: What will happen? Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Wednesday, February 16, 2011
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7 Entry game (cont.) Game theory A game tree: What will happen? Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Wednesday, February 16, 2011
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8 Entry game (cont.) Game theory A game tree: What will happen? Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Wednesday, February 16, 2011
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9 Entry game (cont.) Game theory A game tree: The incumbent firm realizes that if it fights then the entrant will be intimidated and will not enter. This will make the firm obtain payoffs of 8. If they do not fight, the entrant will enter, giving the incumbent payoffs of 5. So the firm is better off fighting, and the entrant will not enter. Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Wednesday, February 16, 2011
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10 Entry game (cont.) Game theory What is a strategy for the entrant? How can we describe the entrant’s strategy when sometimes she chooses one thing and sometimes she chooses another? With sequential games, a strategy is a fully-specified contingent plan. In this example, it specifies two choices for the entrant: what to do if the incumbent fights and what to do if the incumbent does not fight.
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