Consider a 2 player game in which every player has two pure strategies. Which of the following is FALSE? O A If expected utility of an agent i from pure strategy aj is strictly higher than her expected utility from her pure strategy bị given an opponent mixed strategy s.j, then aj is the unique best resonse of agent i to S.j is aj. O B. If expected utility of an agent i from pure strategy aj is equal to her expected utility from her pure strategy bj given an opponent mixed strategy s.j, then agent i has a mixed strategy that is a best response of agent i to s.j. O Cif an agent i has a dominat pure strategy, then the expected utility of agent i from this dominant strategy is strcitly higher than her other pure startegy for all mixed strategies of her opponent.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter18: Asymmetric Information
Section: Chapter Questions
Problem 18.1P
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Consider a 2 player game in which every player has two pure strategies. Which of the following is FALSE?
A. If expected utility of an agent i from pure strategy aj is strictly higher than her expected utility from her pure strategy bj given an opponent mixed strategy s.j,
then aj is the unique best resonse of agent i to s-j is aj.
В.
If expected utility of an agent i from pure strategy aj is equal to her expected utility from her pure strategy bị given an opponent mixed strategy s-j , then
agent i has a mixed strategy that is a best response of agent i to S.j.
If an agent i has a dominat pure strategy, then the expected utility of agent i from this dominant strategy is strcitly higher than her other pure startegy for all
mixed strategies of her opponent.
Transcribed Image Text:Consider a 2 player game in which every player has two pure strategies. Which of the following is FALSE? A. If expected utility of an agent i from pure strategy aj is strictly higher than her expected utility from her pure strategy bj given an opponent mixed strategy s.j, then aj is the unique best resonse of agent i to s-j is aj. В. If expected utility of an agent i from pure strategy aj is equal to her expected utility from her pure strategy bị given an opponent mixed strategy s-j , then agent i has a mixed strategy that is a best response of agent i to S.j. If an agent i has a dominat pure strategy, then the expected utility of agent i from this dominant strategy is strcitly higher than her other pure startegy for all mixed strategies of her opponent.
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