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3.a. What are Firm I's possible strategies? And what are Firm E's possible strategies? 3.b. With the help of strategies, write down the normal form representation of the game. 3.c. Write down the representation of the two firms' mixed strategy.

3.a. What are Firm I's possible strategies? And what are Firm E's possible strategies? 3.b. With the help of strategies, write down the normal form representation of the game. 3.c. Write down the representation of the two firms' mixed strategy.

Principles of Microeconomics (MindTap Course List)
Principles of Microeconomics (MindTap Course List)
8th Edition
ISBN:9781305971493
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Oligopoly
Section: Chapter Questions
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3. Strategic Interactions Consider the following two-player game with imperfect information. (0,10) Out Out (6,4) Firm I Ima In Fight (2,-2) Firm I Firm E 2 Inz (4,4) Out, (5,5) Accommodate In Fight (2,-2) Firm I Accommodate (-2,4) 3.a. What are Firm I's possible strategies? And what are Firm E's possible strategies? 3.b. With the help of strategies, write down the normal form representation of the game. 3.c. Write down the representation of the two firms' mixed strategy. 3.d. Show that for any behavior strategy that Firm I might play, there is a realization equivalent mixed strategy that is, a mixed strategy that generates the same probability distribution over the terminal nodes for any mixed strategy choice by Firm E. 3.e. Does the game have any pure strategy Nash Equilibrium(s)? If so, find them. 3.f. Does the game have any mixed strategy Nash Equilibrium(s)? If so, find them. 3.e. Find all the subgames of this game. 3.h. Does the game have any pure strategy Subgame Perfect Nash Equilibrium(s)? If so, find them. 3.1. Can you add an information set to the game, so that it no longer satisfies perfect recall? If possible, provide one example. If not possible, justify why. 3.j. Can you introduce Nature and modify the game tree so that it represents a game with incomplete information? There are many ways of designing this, providing one example would be sufficient.
Transcribed Image Text:3. Strategic Interactions Consider the following two-player game with imperfect information. (0,10) Out Out (6,4) Firm I Ima In Fight (2,-2) Firm I Firm E 2 Inz (4,4) Out, (5,5) Accommodate In Fight (2,-2) Firm I Accommodate (-2,4) 3.a. What are Firm I's possible strategies? And what are Firm E's possible strategies? 3.b. With the help of strategies, write down the normal form representation of the game. 3.c. Write down the representation of the two firms' mixed strategy. 3.d. Show that for any behavior strategy that Firm I might play, there is a realization equivalent mixed strategy that is, a mixed strategy that generates the same probability distribution over the terminal nodes for any mixed strategy choice by Firm E. 3.e. Does the game have any pure strategy Nash Equilibrium(s)? If so, find them. 3.f. Does the game have any mixed strategy Nash Equilibrium(s)? If so, find them. 3.e. Find all the subgames of this game. 3.h. Does the game have any pure strategy Subgame Perfect Nash Equilibrium(s)? If so, find them. 3.1. Can you add an information set to the game, so that it no longer satisfies perfect recall? If possible, provide one example. If not possible, justify why. 3.j. Can you introduce Nature and modify the game tree so that it represents a game with incomplete information? There are many ways of designing this, providing one example would be sufficient.
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