MATH331 – HOMEWORK 3
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MATH331 – HOMEWORK 3
1. a) State the Expected Utility Proposition (EUP).
(Assume EUP holds in parts b) and c) of this past exam question.)
b) Suppose () is a Simon’s utility function for winning £ , where (−10) = −10 and (100) = 100. Simon sometimes plays Poker or Roulette at his local social club. Both games require a £10 stake to participate. Normally, he is indifferent competing in the Poker game, which gives him a 25% chance of winning £100, and trying his luck on the Roulette wheel with a probability of winning £200. However, for this month only, the club is denoting an extra £100 cash prize into the Poker game, in order to try and recruit new members. For Simon, this makes competing in the Poker game twice as attractive as playing Roulette. Calculate the value of and the utility that Simon places on winning £200.
c) Simon’s club is situated in Liverpool City centre, whilst he lives on the Wirral. He has three modes of transport for travelling to the venue.
= drives in his car through the Mersey tunnel
= catches the ferry over the Mersey
= takes the Merseyrail train service
During the year his mode of transport is summarised by four lotteries, covering the four seasons.
Winter (November to February), = [ , ].
Spring (March to April), = [ , ].
Summer (May to August), = [, (1 − )], where ∈ [0, 1].
Autumn (September to October), = [ , ].
His preference relations regarding these transport lotteries are as follows:
~ and ~ .
Simon’s utility values, denoted by (), () and () for his respective modes of transport, are all positive, and he prefers travelling by car over to the taking the Merseyrail train, because () = (). Calculate the value of and determine which mode of transport he uses most frequently during the year.
2. Eliminate the dominated strategies from the game with payoffmatrices:
( )
( )
for A and B respectively. Then find the Nash equilibria ofthe game.
2022-03-19