Consider the following trust network with shopper A and shops S $=\{$S$1,$S$2,$S$3,$S$4\}.$

Assume that the initial trust ratings are tau$($S$1)=2,$ tau$($S$2)=3,$ tau$($S$3)=2$ and tau$($S$4)=0.$

a$)$ Calculate the trust rating updates after each transaction when A is using services from

$($S$1($satisfactory$),$

S$4($satisfactory$),$

S$1($not satisfactory$),$

S$2($satisfactory$),$

S$2($satisfactory$),$

S$1($satisfactory$),$

S$3($satisfactory$),$

S$2($satisfactory$))$

b$)$ How likely is A to choose the above sequence of transactions $($assume that alpha $=10\%)$

c$)$ What would be the most likely sequence of transactions if you assume that only every third transaction

is not satisfactory?

d$)$ How likely is A to choose the sequence of transactions from c$)?-($assume that alpha $=10\%)$