5. In the lecture, we have shown the following: Theorem: Suppose strategy s, (in a finite game) is strictly dominated by strat- egy ŝ; when opponents are restricted to using pure strategies. That is, Then strategy s, will never be in the support of a best response. That is, for all 0-i o; €BR;(G-;) = 0;(s})=0. (a) Use this result to find all the Nash equilibria (including mixed strategy ones) of the following game. player 2 L R T 10,5 4,1 player 1 M 6,1 8,8 B 5,0 0,10

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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(b) The above theorem holds even when s; is strictly dominated by a mixed
strategy. That is, when there is some ở; such that
7,(ðj,8-;) > A;(8',8-;) Vs-i €S-i.
Use this result to find all the Nash equilibria (including mixed strategy
ones) of the following game.
player 2
L
R
T 8,1
0,0
player 1 M 4,0 12,2
в 6,0 5,10
Transcribed Image Text:(b) The above theorem holds even when s; is strictly dominated by a mixed strategy. That is, when there is some ở; such that 7,(ðj,8-;) > A;(8',8-;) Vs-i €S-i. Use this result to find all the Nash equilibria (including mixed strategy ones) of the following game. player 2 L R T 8,1 0,0 player 1 M 4,0 12,2 в 6,0 5,10
5. In the lecture, we have shown the following:
Theorem: Suppose strategy s, (in a finite game) is strictly dominated by strat-
egy ŝ; when opponents are restricted to using pure strategies. That is,
Then strategy s, will never be in the support of a best response. That is, for all
0-i,
o; € BR;(0-;) =0;(s') = 0.
(a) Use this result to find all the Nash equilibria (including mixed strategy
ones) of the following game.
player 2
R
T 10,5 4,1
м 6,1
8,8
5,0 0,10
player 1
В
Transcribed Image Text:5. In the lecture, we have shown the following: Theorem: Suppose strategy s, (in a finite game) is strictly dominated by strat- egy ŝ; when opponents are restricted to using pure strategies. That is, Then strategy s, will never be in the support of a best response. That is, for all 0-i, o; € BR;(0-;) =0;(s') = 0. (a) Use this result to find all the Nash equilibria (including mixed strategy ones) of the following game. player 2 R T 10,5 4,1 м 6,1 8,8 5,0 0,10 player 1 В
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