Note: solution should not be hand written. 3. Strategic InteractionsConsider the following two-player game with imperfect information.(0,10)OutOut(6,4)Firm IImaInFight(2,-2)Firm IFirm E2Inz(4,4)Out,(5,5)AccommodateInFight(2,-2)Firm IAccommodate(-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 equivalentmixed strategy that is, a mixed strategy that generates the same probability distribution overthe 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, findthem.3.1. Can you add an information set to the game, so that it no longer satisfies perfect recall? Ifpossible, 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 withincomplete information? There are many ways of designing this, providing one example wouldbe sufficient.

Imperfect information game is a type of sequential game theory, where among the opponent players,…

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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Question

Note: solution should not be hand written.

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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