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## INTRO GAME THEORY

by: Arno Leuschke

45

0

3

# INTRO GAME THEORY ECON 171

Arno Leuschke
UCSB
GPA 3.66

G. Charness

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COURSE
PROF.
G. Charness
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

## Popular in Economcs

This 3 page Class Notes was uploaded by Arno Leuschke on Thursday October 22, 2015. The Class Notes belongs to ECON 171 at University of California Santa Barbara taught by G. Charness in Fall. Since its upload, it has received 45 views. For similar materials see /class/227149/econ-171-university-of-california-santa-barbara in Economcs at University of California Santa Barbara.

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Date Created: 10/22/15
6 Dominance and Best Response 1 a B dominates A and L dominates R b L dominates R c 23 U 13 D dominates M X dominates Z d none a To determine the BR set we must determine which strategy of player 1 yields the highest payoff given her belief about player 27s strategy selec tion Thus7 we compare the payoff to each of her possible strategies u1U021310 O 133 133 u1M021321210136 6 u1D02 133134136 133 BR102 M b BR201 L7R C 31131092 Ule d BR201 0 Player 1 solves maxq1 100 7 211 7 2q2q1 7 2011 The rst order condition is 100 7 4q1 7 2q2 7 20 0 Solving for 11 yields BR1q2 20 7 122 It is easy to see that 31310 20 Since qz 2 07 it cannot be that 25 is ever a best response Given the beliefs7 player 17s best response is 15 a First we nd the expected payoff to each strategy LL1U 02 260 412 73 u1M02 31612 1 and u1D021611 136 As the strategy U yields a higher expected payoff to player 17 given 02 BR102 b BR201 c BR1lt02gt 7 U d BR102 U D e 313201 L R 84 Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 6 DOMINANCE AND BEST RESPONSE 85 5 2 1 R P S R 0 0 l I 1 1 P l 0 0 4 S ll 1 1 00 3 BR162 P b 33192 R S c BR162 P d 3mm 51 6 No This is because 12 A 12 B dominates C 7 M is dominated by 137 2370 8 From exercise 37 BR1q2 20 122 SO UD1 07 20 Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute 7 Rationalizability and Iterated Dominance 1 a R U M D x L R b Here there is a dominant strategy So we can iteratively delete dom inated strategies U dominates D When D is ruled out7 R dominates C Thus7 R U7 M x L7 R 01 3 U7 L d R A7 B x X7 Y e R A7 B x X7 Y f R A7 B x X7 Y 0 R D Y For give in77 to be rationalizable7 it must be that x g 0 The man ager must believe that the probability that the employee plays settle is weakly greater than 12 H x7 The order does not matter because if a strategy is domi nated not a best response relative to some set of strategies of the other player7 then this strategy will also be dominated relative to a smaller set of strategies for the other player R 700 600 600 Instructors39 Manual for Strategy Copyright 2002 2008 by Joel Watson An Introduction to Game Theory For instructors only do not distribute

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