class14_repeatedGame_

# class14_repeatedGame_ - Econ 51, Winter 2011 Class #14...

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1 Econ 51, Winter 2011 Class #14 Today: Finish sequential and repeated games. Start applications of game theory. Tuesday, February 22, 2011

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2 Review of extensive-form games Game theory A sequential game (or extensive-form game ) is a game in which players play in sequence (over time), with the action of each turn realized (and observed by others) before other players take their actions. In sequential games, the subgame perfect equilibrium (SPE) is an appropriate solution concept. An SPE is a Nash equilibrium of the game, such that the equilibrium strategies constitute a Nash equilibrium of every subgame of the game. The point of this definition is to prohibit empty threats . A very simple algorithm to find an SPE is called backward induction : solve the problem from the end of the game and proceed back to the beginning of the game. Tuesday, February 22, 2011
3 Review: Entry game Game theory Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Tuesday, February 22, 2011

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4 Review: Entry game Game theory In backward induction, begin with the last period: In the subgame after the incumbent fights, the entrant stays out. Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Tuesday, February 22, 2011
5 Review: Entry game Game theory We should also look at a subgame after the incumbent does not fight. In this subgame, the entrant enters. Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Tuesday, February 22, 2011

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6 Review: Entry game Game theory Now look at the first period: The incumbent firm realizes that if it fights then the entrant will be intimidated and will not enter. Incumbent Entrant Entrant (2, -2) (8, 0) (5,5) (10, 0) Fight Not Fight Enter Enter Stay out Stay out Tuesday, February 22, 2011
7 Review: Entry game Game theory Now look at the first period: The incumbent firm realizes that if it fights then the entrant will be intimidated and will not enter. So the firm chooses to fight, 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 Tuesday, February 22, 2011

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8 Repeated Games Using the SPE concept, we will then analyze repeated games. Tuesday, February 22, 2011
9 Repeated games Game theory Study of repeated games is an important application of SPNE. The main theme: repeated interaction is prevalent in many social situations. We meet the same friends over and over again and attend 20 lectures of a course, firms face the same competitors in the industry, etc. People may cooperate now, in the hope that cooperation can be sustained in the future. Thus negative predictions of theory of simultaneous games

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## This note was uploaded on 03/19/2011 for the course ECON 51 taught by Professor Tendall,m during the Winter '07 term at Stanford.

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class14_repeatedGame_ - Econ 51, Winter 2011 Class #14...

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