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Lecture

Topic 7 - Extensive Form Games - Bargaining.pdf

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Department
Economics
Course
ECO326H1
Professor
Marcin Peski
Semester
Fall

Description
Topic 7 – Extensive Forms Games: Bargaining Nov 5 , 2012 (Chapter 7.1-7.2, 7.6-7.7) Last Lecture: Definition: An Extensive Form Nash Equilibrium is a profile of extensive form strategies that are mutual best responses in the original game.  Example 1: Apple Two Nash Equilibriums: (In, Accommodate if In) Accommodate Fight (Out, Fight if Out) ( ) ( ) Subgame after history - The same set of players - The same set of actions - Histories such that is a continuation of Definition: A Subgame Perfect Equilibrium (SPE) is a profile of strategies that induce a Nash Equilibrium / i.e. they are mutual best responses in every Subgame. - Initial game = Subgame after ; - Every SPE is NE; - NOT every NE is SPE Refer to example 1: - (In, Accommodate if In) is a SPE, also an NE in the subgame , also an NE in the subgame {In}; - However, (Out, Fight if Out) is not a NE in the subgame {In}, therefore it is a NE not a SPE.  Example 2 – Ultimatum Game - Two Players Player 1 - Player 1 makes an offer - Player 2 either: 𝑥 Accepts: Payoff Player 2 Rejects: Payoff Accepts Rejects 𝑥 𝑥 Subgame after history , player 2 best responses: - Accepts if - Rejects if There is a unique SPE in the ultimatum game: - Player 1 offers ; - Player 2 accepts after ANY offer  Example 3 – Two Period Bargaining (A. Rubinstein) Period 1: Player 1 makes an offer (Pie size = 1) Player 2 Accepts or Rejects. If Player 2 rejects: Period 2: Player 2 makes a counter offer (Pie size = ) Player 1 Accepts or Rejects. If Player 1 rejects: game ends. Player 1 Player 2 Accepts Rejects Player 2 Player 1 Accepts Rejects 1. Subgame - SPE is player 2 offers and player 1 accepts always. 2. Erase the solved subgame – determined the unique payoff in that subgame, substitute that payoff into the game. Player 1 Player 2 Accepts Rejects 3. In this game, SPE is: - Player 1 offers , - Player 2 accepts if rejects if - Unique payoff:  Example 4 – Three Period Bargaining - Order of offers: Player 1, Player 2, Player 1 - Value of the pie: Player 1 Player 2 Accepts Rejects Player 2 Player 1 Accepts Rejects Player 1 Player 2
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