2. Consider the following variation to the Rock (R), Paper (P),Scissors (S) game:Suppose that with probability p player 1 faces a Normal opponent and with probability 1-p, he faces a Simple opponent that will always play P.Player 2 knows whether he is Normal or Simple, but player 1 does not.·The payoffs are pictured in the payoff matrices below:Normal1\2RPSR0,0-1,11,-1P1,-10,0-1,1S-1,11,-10,0with probability pSimple1\2RPSP-1,10,01,-1 with probability 1-p.Suppose p = 1/3, select all pure strategy Bayesian equilibria (there may be more than one):(Form: 1's strategy; 2's type - 2's strategy)a) (S; Normal - P, Simple - P)b) (R; Normal - P, Simple - P)c) (S; Normal - R, Simple - P)d) (P; Normal - P, Simple - P)

Given: The probability of Normal play is 1/3 The probability of Simple play is 2/3

Suppose p = 1/3, select all pure strategy Bayesian equilibria (there may be more than one): (Form: 1's strategy; 2's type - 2's strategy) a) (S; Normal - P, Simple - P) b) (R; Normal - P, Simple - P) c) (S; Normal - R, Simple - P) d) (P; Normal - P, Simple - P)

Suppose p = 1/3, select all pure strategy Bayesian equilibria (there may be more than one): (Form: 1's strategy; 2's type - 2's strategy) a) (S; Normal - P, Simple - P) b) (R; Normal - P, Simple - P) c) (S; Normal - R, Simple - P) d) (P; Normal - P, Simple - P)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

2. Consider the following variation to the Rock (R), Paper (P),Scissors (S) game:
Suppose that with probability p player 1 faces a Normal opponent and with probability 1-p, he faces a Simple opponent that will always play P.
Player 2 knows whether he is Normal or Simple, but player 1 does not.
·
The payoffs are pictured in the payoff matrices below:
Normal
1\2
R
P
S
R
0,0
-1,1
1,-1
P
1,-1
0,0
-1,1
S
-1,1
1,-1
0,0
with probability p
Simple
1\2
R
P
S
P
-1,1
0,0
1,-1

with probability 1-p.
Suppose p = 1/3, select all pure strategy Bayesian equilibria (there may be more than one):
(Form: 1's strategy; 2's type - 2's strategy)
a) (S; Normal - P, Simple - P)
b) (R; Normal - P, Simple - P)
c) (S; Normal - R, Simple - P)
d) (P; Normal - P, Simple - P)

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