You and I play the following game. Hidden from you, I put a coin in my hand: with probability p it is a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand: you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin. You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p and 8) is your expected gain in pence from playing this game once with me? Challenge: suppose we are going to play repeatedly and you want to maximise your gain and I wish to minimise my loss. What value of p should I choose and what value of s should you choose? (This question is somewhat ill-defined, but it does have an interesting possible answer.) (Note: anything labelled "challenge" will not be part of the hand-in.)

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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You and I play the following game. Hidden from you, I put a coin in my hand: with probability p it
is a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand:
you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin.
You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p and
s) is your expected gain in pence from playing this game once with me?
Challenge: suppose we are going to play repeatedly and you want to maximise your gain and I
wish to minimise my loss. What value of p should I choose and what value of s should you
choose? (This question is somewhat ill-defined, but it does have an interesting possible answer.)
(Note: anything labelled "challenge" will not be part of the hand-in.)
Transcribed Image Text:You and I play the following game. Hidden from you, I put a coin in my hand: with probability p it is a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand: you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin. You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p and s) is your expected gain in pence from playing this game once with me? Challenge: suppose we are going to play repeatedly and you want to maximise your gain and I wish to minimise my loss. What value of p should I choose and what value of s should you choose? (This question is somewhat ill-defined, but it does have an interesting possible answer.) (Note: anything labelled "challenge" will not be part of the hand-in.)
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